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Although the D4-D5-E6-E7-E8 VoDouPhysics model is NOT a SuperStringTheory, the nice math involved in StringTheory is relevant, although not as a "theoryof elementary particles". In theD4-D5-E6-E7-E8 VoDou Physics model, closed strings representthe world-lines of fermion particle-antiparticle pairs( the pair of fermions acting as a boson so thatthe entire string is bosonic ) from the time of theircreation to their eventual mutual annihilation(perhaps with lots of interactions with lots of otherparticles/antiparticles of other world-lines in the meantime, andwith mutual creation/annihilation guaranteed by considering StringTheory spacetime to be a compactified 25+1 dimensional Minkowskispacetime).

The D4-D5-E6-E7-E8 VoDou Physicsmodel has:

whose Geometric and PhysicalInterpretations are:

Algebraic formulation ofBohm-many-worlds string quantum theory, timelike brane M-theory, andspacelike brane F-theory may be useful in sum-over-historiesinterpretations, particularly with respect to primenumbers and zeta functions.

Such String, M, and F Theories are used in my QuantumConsciousness paper contributed toQuantum Mind 2003.

26-dimensional String Theory and 27-dimensional M-theory can be represented by 3x3 Hermitian octonion matrices of the form:
a Y X Y* b Z X* Z* c
where X, Y, Z are 8-dim octonions, * is conjugation, anda, b, c are real numbers, which are independent for 27-dim M-theory,in which case they form the 27-dim Jordan algebra J3(O)andwhich sum to zero for 26-dim string theory in which case theyform the 26-dim traceless part J3(O)o of that Jordan algebra.THE X, Y, Z COORDINATES FORM A CONFIGURATION SPACE for 1-particle states,in that, for a given 1 fermion particle:the octonion X determines a position in 4-dim spacetime and                                     in 4-dim internal symmetry space;the octonion Y determines an identity as a fermion particle;the octonion Z determines an identity as a fermion antiparticle.The real numbers a, b, c are Auxiliary variables.27-dimensional M-theory and 28-dimensional F-theory can be represented by 4x4 quaternion Hermitian matrices of the form:
a U T R U* b S V T* S* c W R* V* W* d
Here R, S, T, U, V, W are quaternions, * is conjugation, and a, b, c, d, are real numbers, andTHE R, S, T, U, V, W COORDINATES FORM A CONFIGURATION SPACE for 1-particle states, in that, for a given 1 fermion particle:the quaternion R determines a position in 4-dim spacetime;the quaternion S determines in 4-dim internal symmetry space;the quaternion pair T, U determines an identity as a fermion particle;the quaternion pair V, W determines an identity as a fermion antiparticle.The real numbers a, b, c, d are Auxiliary variables.In this case, the 4x4 quaternion Hermitian matrices form theJordan algebra J4(Q) (where I use Q to denote quaternion),andthe theory is like A 28-DIM F-THEORY (if you recall, in the stringtheory community a few years ago F-theory was popular as a"generalization" of M-theory, with 1 more dimension than M-theory.27-DIM M-theory itself can also be seen in terms of quaternions, by using the traceless J4(Q)o instead of J3(O). 

Here are the Geometrical andPhysical interpretations of:


Jordan algebra Lie algebra Sphere structure symmetry structure
26-dim Strings J3(O)o E6 / F4 Real S0 = {-1,+1} is boundary 78-52 = 26 of String Interval [-1,+1] ( closed string if you identify -1 = +1 ) (Compare Graded Lie Algebra structure.)
 
In the D4-D5-E6-E7-E8 VoDou Physics model, closed strings represent the world-lines of fermion particle-antiparticle pairs ( the pair of fermions acting as a boson so that the entire string is bosonic ) from the time of their creation to their eventual mutual annihilation,
   *    / \   ... /   \ //     |         (The illustrated closed string is red.\     |          It interacts with a partially shown gray string.) \   / \...  \ /    *  
perhaps with lots of interactions with lots of other particles/antiparticles of other world-lines in the meantime, so that part of each string might represent a photon or other particle of any type formed by interaction of one of the particle/antiparticle pair.

Note that since our Universe began with a Big Bang, all its particles originate from pair creation since then. For pairs that do not appear to reconnect for mutual annihilation within the volume of 26-dimensional spacetime being considered in working with the String Theory,

****************    \    ...   /   \      \ /    \      |         (The illustrated string is red.     \     |          It interacts with a partially shown gray string.      \   / \...      A perfect absorber in the future         \ /            is indicated by ******* ).        *  
the string is closed by considering the 26-dimensional spacetime to be a compactified 25+1 dimensional Minkowski spacetime due to considering the Universe to "... be a perfect absorber in the future ...[as in]... the Wheeler-Feynman ... absorber theory of radiation ..." described by Narlikar in his book Introduction to Cosmology (Cambridge 1997) (Section 8.8.1) and related to the Collective Electrodynamics of Carver Mead. For most of the matter in our Galactic Cluster, such an absorber could be a Black Hole of the Black Hole Era. Such a compactification is also similar to the conformally compactified 3+1 dimensional Minkowski spacetime M# used by Penrose and Rindler in their book Spinors and Space-Time, Volume 2 (Cambridge 1986) (particularly Chapter 9). ]]

 

These Strings look like "world-line paths" of fermions in"configuration space-time" and their String Theory is the way tocalculate the Generalized Bohm Quantum Potential that "tells" thefermion how to "move around" in configuration space is itself actedback on by the Fermion Configuration.

The Quantum Theory of the D4-D5-E6-E7-E8VoDou Physics model has several ( in my opinion equivalent )formulations, including Many-Worlds,Nelson's Stochastic Theory, andgeneralized Bohm Quantum Theory. Inthe generalized Bohmian point of view

"states of the physics model" are viewed as being completely determined by"configurations of fermions in configuration space",
which is consistent with the lattice physics view that
fermions live on vertices of the lattice, andgauge bosons live on links of the lattice,

so that gauge bosons can be represented in terms of fermions bythe "state" of one fermion at the beginning of a link and of anotherfermion on a vertex at the end of a link, and composite bosons (likepions, which are pairs of quarks) can be represented in terms oftheir constituent fermions.

In other words, 26-dim String Theory can be interpreted as beingthe theory of movement of a "Bohm Point" in configuration space. (Since I like to use a Lagrangian formulation using spacetime asopposed to a Hamiltonian spatial formulation with time as an"outside" variable, the configuration space is not particle positions(points) in fermion representation spaces, internal symmetry space,and spatial space but is particle world-lines (strings) in fermionrepresentation spaces, internal symmetry space, and spacetimeincluding both spatial dimensions and time dimension. )

If you look at String Theory as being analogous to GeneralRelativity of a 26-dimensional SpaceTime, then you see that

so that the Quantum Theory is, like General Relativity, NonLinearin that the Generalized Bohm Quantum Potential (compare Gravitation)acts on the Configurations (compare Matter Fields) and theConfigurations (compare Matter Fields) also act (by what JackSarfatti calls Post-Quantum Back-Reaction) on the GeneralizedBohm Quantum Potential (compare Gravitation).


Jordan algebra Lie algebra Sphere structure symmetry structure


27-dim M-Theory J3(O) E7 / E6xU(1) Complex S1 is boundary J4(Q)o 133-78-1 = 54 = 2x27 of Unit Disk = 2-ball B2 Time Part of (2,4) vector space of Conformal Spin(2,4)(Compare Graded Lie Algebra structure.)
 

The (2,4) Conformal vector spacecorresponds to 6 of the 10 dimensionsof the vector representation of the D5Lie algebra of the D4-D5-E6-E7-E8 VoDouPhysics Model. On those 6 dimensions, the ConformalGroup Spin(2,4) = SU(2,2) acts linearly. The correspondingsubspace of the 8 dimensions of the vector representation of theD4 Lie algebra of the D4-D5-E6-E7-E8VoDou Physics Model is 4-dimensional PhysicalSpaceTime, on which the Conformal Groupacts non-linearly.

The 2-ball B2 corresponds to the 2 Timelike dimensions of (2,4)Conformally Linear PhysicalSpaceTime.

The S1 boundary of B2 corresponds to the 1 Timelike dimension of(1,3) 4-dimensional ( Conformallynon-linear) Physical SpaceTime.

These Timelike spaces look like p-Brane Membranes and theirM-theory describesinteractions among the Timelike parts of parallel material BraneUniverses that Jack Sarfattidescribes (in Decenber 2001 e-mail correspondence) as being "...next door to each other across thinJosephson tunnel "weak link" junctions in which Star Gates form...".


Jordan algebra Lie algebra Sphere structure symmetry structure


28-dim F-Theory J4(Q) E8 / E7xSU(2) Quaternion S3 is boundary 248-133-3 = 112 = 4x28 of 4-ball B4 Spatial Part of (2,4) vector space of Conformal Spin(2,4)(Compare Graded Lie Algebra structure.)
 

The 4-ball B4 corresponds to the 4 Spacelike dimensions of (2,4)Conformally Linear PhysicalSpaceTime.

The S3 boundary of B4 corresponds to the 3 Spacelike dimension of(1,3) 4-dimensional ( Conformallynon-linear) Physical SpaceTime.

These Spacelike spaces look like p-Brane Membranes and theirF-theory describesinteractions among the Spacelike parts of parallel material BraneUniverses that Jack Sarfattidescribes (in Decenber 2001 e-mail correspondence) as being "...next door to each other across thinJosephson tunnel "weak link" junctions in which Star Gates form...".


Jack Sarfatti describes(in Decenber 2001 e-mail correspondence) "...The parallel material "brane universes", next door to eachother across thin Josephson tunnel "weak link" junctions in whichStar Gates form ...". If you consider that newUniverses might form from Quantum Fluctuations in olderUniverses, you can see that it might be reasonable to expect thatmany Parallel Material Universes ( one of which might be OurUniverse ) might exist very close to each other, or intersect witheach other at Intersection StarGates.

Consider the following illustration, adapted from anAnn Feild STScI illustration of a Model of ExpandingUniverse:

The illustration shows only 3 levels of Universes, and so is muchsimpler than reality.

The illustration is a 2-dimensional projection of an embeddinginto 3 dimensions of a 2-dimensional ( 1 timelike, 1 spacelike )universe, with only 2 spacelike dimensions of 4-dimensionalPhysical SpaceTime being suppressed, and so is probably notunreasonably unrealistic ( just replace a S1 circle "horizontal"cross-section of each universe with an S3 3-sphere ) if you restrictyour viewpoint to only the 4 dimensions of 4-dimensionalPhysical SpaceTime.

However, for 27-dimensionalJ4(Q)o M-theory and 28-dimensional J4(Q) F-theory, another 23 (forJ4(Q)o M-theory) and 24 (for J4(Q) F-theory) dimensions aresuppressed in the illustration.

Could those 23 or 24degrees of freedom provide enough separation among theUniverses so that they are not really very close to, or intersectingwith, each other? To answer that question, consider the physicalnature of those 23 or 24 degrees of freedom within thestructure of the Jordan algebra J4(Q) of 4x4 Quaternionic Hermitianmatrices:

a U T R U* b S V T* S* c W R* V* W* d

Here R, S, T, U, V, W are quaternions, * is conjugation, and a, b,c, d, are real numbers, and:

The dimensions of the 4-dimensional Physical SpaceTime that formthe viewpoint of the above illustration of closeneighbor/intersecting Universes are Large ( with respect to humanexperience ) Dimensions.

If the other 24 ( or 23 if a, b, c, d are notindependent, as in 27-dimensional J4(Q)o M-theory ) dimensionsare also Large, then maybe they could provide enough room forseparation among the Universes so that they are not really very closeto, or intersecting with, each other. Therefore, we need to ask:How Large are thoseother 24 dimensions?

 

 

 

Therefore, only at most 6

( auxiliary a, b, c, d andneutrino S1 and antineutrino S1)

of the other 24( or 5 of the other 23 if a, b, c, d are notindependent, as in 27-dimensional J4(Q)o M-theory )dimensions might be Larger than 10^(-16)cm.

 

Note that none of the Size-Scale upper bounds are smallerthan the scale of the Self-DualEnergy Region of SU(5) Duality, which is about 10^17 eV = 10^8GeV = 10^(-22) cm.

 

Gravity at Various Size-Scales:

 

 

 

 

 


 

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