The Theory Page
Theory Continued Page
Theory Continued page 2
Theory Continued page 3
Theory Continued Page 4
Accelerated Expansion and the ZPF
Resource Links Page
Some Other problems this theory deals with.
One problem early String Theory of the open String type had was with the Quark and Anti-Quark models. Since a String was originally a 1D and latter,2D membrane it had only two ends. One could not have 3 Quarks on it. By utilizing an idea from TGD theory , and replacing the 2D open String with a 10D closed string composed of two subsets or subspaces one arrives at a system whose case boundries form small holes in the 4D space-time continum. This allows the outer vibrating 4D membrane to loop into the inner positive 6D vibrating membrane. Thus, the system becomes a self-sustaining unit. As, such, it generates its own field. This explains an early discovery from standard field theory first noted with the EM field.
With this sort of space-time manifold the vibrational frequency and wavelength determines what manifestation the gravitons will take. Now, for a moment I must first discuss a specific type of manifold that normal string theory deals with. A Calabi-Yau variety of dimension d is a complex manifold with trivial canonical bundle and vanishing Hodge numbers h i,0 for 0 < i < d. For instance, a dimension 1 Calabi-Yau variety is an elliptic curve, a dimension 2 Calabi-Yau variety is a K3 surface, and a dimension 3 is a Calabi-Yau threefold.
One of the most significant developments in the last decade in Theoretical Physics (High Energy) is, arguably, string theory and mirror symmetry. String theory proposes a model for the physical world which purports its fundamental constituents as 1 or 2-dimensional mathematical objects "strings" rather than 0- dimensional objects "points". Mirror symmetry is a conjecture in string theory that certain "mirror pairs" of Calabi-Yau manifolds give rise to isomorphic physical theories. Calabi-Yau manifolds appear in the theory because in passing from the 10-dimensional space time to a physically realistic description in four dimension, string theory requires that the additional 6-dimensional space is to be a Calabi-Yau manifold.
It is the added four degrees of movement that 6D Higgs space-time allows that determine the Mass,Charge, and Spin of any given particle
Now, the throats of the coupling points form wormholes. They have a charge flow that is equal to the value of the specific particle involved. Gravity is determined by the amount of torsion 4D space-time places upon the 6D component.
Thus, this is why this system, while having the graviton in all of its mutated forms be the carrier. Does restore the simplistic nature of General Relativity back into the equation.
However, there is still one problem with GR that must be dwelt with.
One problem with General Relativity.
In General Relativity, the density of matter and the stress in it are determined equal to a certain combination of derivaties of Christoffel symbols. The Theory requires an indefinite metric called the Minkowski Metric. By it time-like seperations are at a positive distance, Space-like(Tachyonic) seperations are of a negative value, and light like are zero. This gives one a typology that by its own nature is not a Hausdorff,Metric, or Riemannian manifold. This is why all equations to get results only stem from ones based on ignoring the topology that the Minkowski Metric induces. Some good results have been arrived at by utilizing a Klien topology. This theory, as with standard M-Theory, follows that same line of thought.
GENERAL TERMS AND KODAIRA'S THEORY.
Terms in usage below.
For functions f(x1) or r(x1, x2) of one or multiple points respectively:
The ordinary derivative of f in the direction of coordinate number i.
The covariant derivative of f in direction i. It would differ from the ordinary derivative only if f had a composite value, i.e. vector or matrix valued rather than scalar.
r[1!i] or r[2!j]
The ordinary derivative of r in direction i of the first argument, or direction j of the second.
r[1/i] or r[2/j]
Similarly for covariant derivatives.
Consider a curve c(t) on the manifold. For any function f(p) on the manifold, you can get d/dt f(c(t)), the directional derivative. Focus on one point q at a time. Frequently different curves through q will produce the same directional derivative, no matter which function is differentiated -- if the curves are tangent. Thus make equivalence classes among curves (through q). These equivalence classes are called vectors (at q). They form a vector space.
A set of p (in 0 to n) vectors is referred to as a p-vector; it defines an element of area (p = n-1) or volume (p = n). The vectors in a p-vector are combined antisymmetrically with the Grassman product such that v^w = -w^v.
A linear functional on p-vectors is called a p-form. While the value of a form (when a vector is fed to it) is typically a scalar, a composite object (form or vector or matrix) could also be the value. Forms can also be combined with the Grassman product. Any function f (defined at point q) defines a 1-form at q, the gradient of f, wherein the argument vector takes the directional derivative of the function, and the coordinate functions define a basis of all the 1-forms, notated dx[i] (i = 1..n). For calculation, suppose the components of a form A are A[i] and a vector v is v[i]. Then to compute, the functional value A(v) = sum (i = 1..n) A[i]v[i]. This is often abbreviated A.v
Covariant and Contravariant
When a map y(x) from one manifold to another is represented by coordinates, the Jacobian J[i][j] = y[i][!j]. Given a function f(y) and define a new function g(x) = f(y(x)). The gradient df = f[!i], a 1-form. What is the gradient of g? By the chain rule dg[j] = sum (i = 1..n) f[!i] J[i][j]. 1-forms and any composite objects that transform similarly are called ``covariant''. Objects that transform through the inverse of the Jacobian, such as vectors, are called ``contravariant''.
When covariant and contravariant objects appear in the same term they almost always are summed as in the above expression for dg[j]. When the same subscript letter is repeated in a covariant and a contravariant position, summation is assumed but the sum symbol is not actually written.
Metric Dual (represented by *)
For a p-form A, suppose you take its metric product with another p-form B. Point by point, this is a linear functional of p-forms, that is, it is a p-vector. Suppose you wished to integrate the function value relative to the volume element in the space. An alternative way to express the kernel of the integral would be to obtain a (n-p)-form *A and take its Grassman product with B. This is the metric dual of A. It has a simple form: it has the same components (some changing signs) multiplied by G, the positive square root of the determinant of the metric tensor. (It is unclear what the metric dual would be if the determinant were negative.) On an even dimension space, ** (metric dual twice) reverses the sign of odd degree forms but is an identity transformation for even degree forms. In odd dimensions it also either is the identity or reverses the sign, but it's more complicated to determine for which degrees this happens.
A generally similar theorem holds for currents continuous in the mean at infinity. (Meaning: let f[i] be one of a set [i] of forms that are C-infinity and have compact support and (f[i],f[i]) (metric product) is bounded over [i]. A current A is "continuous in the mean at infinity" if A[f[i]] (the functional action or integral) is bounded over [i] for any such set of forms.)
For computing the decomposition: First take the metric product of A with each of a basis of harmonic forms, suitably normalized, and assemble a linear combination thereof having the same metric products; that's A3, and (A - A3) is orthogonal to all harmonic forms. Now integrate Green's function acting on (A - A3) to solve the Fredholm equation.On Rn, Green's function is 1/r(n-1) where r is the distance between the argument points.
Kodaira's theorem and friends were not proved for double currents, matrix-valued currents, etc; only for scalar-valued currents (electric, for example, which is why De Rham called them "currents"). This whole approach, however, assumes that an analog can be produced for matrix-valued currents.
General Relativity Formula.
R[i][j][k][L] = C[j][L][i][!k]
+ C[j][k][m] g'[m][n] C[i][L][n]
- C[j][L][m] g'[m][n] C[i][k][n]
R[j][k] = g'[p][q] R[p][j][k][q]
= g'[i][L] C[j][k][m] g'[m][n] C[i][L][n]
- g'[i][L] C[j][L][m] g'[m][n] C[i][k][n]
+ g'[i][L] C[j][L][i][!k]
- g'[i][L] C[j][k][i][!L]
R = g'[r][s] R[r][s]
= g'[r][s] g'[p][q] R[p][r][s][q]
Einstein's law of gravitation takes the following form:
R[i][k] - 1/2 g[i][k] (R - 2L) = -8pi N T[i][k
T[i][k] is the density of mass and momentum; actually g'[j][i] T[i][k] has the more familiar units. The factor of -8pi N (where N is Newton's gravitational constant) allows T to contain mass and momentum densities where the masses are in kilograms, or whatever mass units were used to determine N. L is the notorious ``cosmological constant''. Presently it is popular to speculate that it has a substantial nonzero value, although Einstein did not have experimental data to fit, and set it zero because that would produce an asymptotically flat space. Matter and momentum are supposed to be conserved:
g[t][u] T[i][t][/u] = 0
If V[i] is the tangent vector to a geodesic, then
0 = V[i][/j]V[j] = V[i][!j]V[j] + V[m] g'[i][n] C[m][j][n] V[j
Here are the equations of motion in coordinate form. V[i] is the zero velocity field.
0 = C[i][j][k][/L] V[L]
= C[i][j][k][!L] V[L]
- C[m][j][k] g'[m][n] C[i][L][n] V[L]
- C[i][m][k] g'[m][n] C[j][L][n] V[L]
- C[i][j][m] g'[m][n] C[k][L][n] V[L]
0 = V[i][/L] V[L]
= V[i][!L] V[L] + V[i] g'[m][n] C[i][L][n] V[L]
These are easily solved for the time derivatives. It is necessary that V[t] be nonzero everywhere.
The connection of a Riemannian manifold is a map from tangent vectors at a point x1 to vectors at another point x2, which tells which vectors are parallel. How can it be derived from the distance function?
Define this matrix-valued function, whose dual will turn out to be the connection: g(x2,x1)[i][j] = -0.5 r2[/x2[i]][/x1[j]]. Here the notation [/x2[i]] means covariant differentiation by coordinate i of x2, and it will be abbreviated [2/i], so g[i][j] = -0.5 r2[2/i][1/j]. However, since r is scalar valued, no covariant corrections appear.
When x1 == x2, the matrix (double 1-form) thus defined is the metric tensor, defining an inner product on vectors. The notation q*h means q[i]g[i][j]h[j] (all factors being colocated).
When x2 != x1, g(x2,x1)[i][j] defines a map from vectors at x1 to 1-forms at x2, and the dual (at x2) of that 1-form (i.e. the vector which, lowered by g(x2,x2), gives the same 1-form) is the image of the x1 vector through a uniquely defined map. Thus a single vector at x1 is propagated to a vector field. Annotate this map as N(x2,x1,v1). It's true that N(x1,x2,N(x2,x1,v1)) == v1, but generally N(x2,x3,N(x3,x1,v1)) != N(x2,x4,N(x4,x1,v1)) (for different x3, x4). This would only be true in a flat space.
Given a path through x1, it has there a tangent p. Another path through x2 has a tangent q. When are the paths parallel? The definition of parallel that Euclid used is that if the paths are straightly extended they will never intersect (in two dimensions). More useful in higher dimensions and lumpy spaces is, if an equal displacement is made along each path (each according to its own parameter), the distance between the path points is stationary in the sense that its second derivative is zero versus the (equal) parameters at x1 and x2. Since we're saying that the paths are parallel only at x1 and x2, we should really say that their tangents p and q are parallel. Now let's express parallelism by a formula. Let R = distance between x1 and x2. Use the same parameter t for both paths, and define Q(t) = distance squared between path points as a function of t. (It is squared because the range space of the metric tensor is distance squared.) Let h(x) = tangent to the geodesic from x1 to x2. In 2nd order,
Q(t) = R2(x2+qt, x1+pt)
= R2(x2,x1) + R2[2/i]q[i]t + R2[1/i]p[i]t (negative)
+ 0.5 R2[2/i][2/j]q[i]q[j]t2 + 0.5 R2[1/i][1/j]p[i]p[j]t2
By definition (?) of what a geodesic is:
h.g.h = 1
R2[2/i] = 2 g(x2,x2).h(x2)
R2[1/i] = -2 g(x1,x1).h(x1)
Let g' represent the inverse of g, and let p' = p mapped by N, that is:
p'[i] = g'(x2,x2)[i][k] g(x2,x1)[k][j] p[j]
Q(t) = R2(x2+qt, x1+pt)
= R2(x2,x1) + 2 q.g(x2,x2).h(x2)t - 2 p.g(x1,x1).h(x1)t
+ (q.g(x2,x2).q + p.g(x1,x1).p - 2 q.g(x2,x1).p)t2
= R2(x2,x1) + 2 (q*h(x2) - p*h(x1)) t
+ (q*q + p*p - 2 q*p')t2
where q*p' uses the metric at x2. Saying that the paths are "parallel" means that R2(t) is constant to 2nd order. That is true when p' == q, which also makes (q*h) == (p*h) and (q*q) == (p*p). (It's necessary that the "speed" of both paths be the same. This isn't Euclid.) In other words, q is parallel to p if map N takes p over to q, showing that the map N, the metric dual of g(x2,x1)[i][j], is the connection.
The connection is also called the geodesic normal map, and mapping by N is also called parallel propagation along the (unique) geodesic between x1 and x2. For each x1 there is a neighborhood such that for all x2 therein, the geodesic between x1 and x2 is unique.
Second covariant derivatives generally are not independent of order, and their commutated value depends linearly on the original tensor, and the coefficients form a matrix-valued 2-form called the Riemann-Christoffel tensor. Its "official" definition is:
A[j][/k][/L] - A[j][/L][/k] = A[m] g'[m][i] R[i][j][k][L]
R[i][j][k][L] = C[j][L][i][!k] + C[j][k][m] g'[m][n] C[i][L][n]
- C[j][k][i][!L] - C[j][L][m] g'[m][n] C[i][k][n]
Let's see if we can get this by formally differentiating the Christoffel symbols as if they were a tensor. It will be seen later that the Christoffel symbols as a matrix-valued 1-form can be uniquely segregated into the sum of a tensor and a maximally non-tensor part, and justification will be given for relegating the latter to oblivion.
Lemma 1: Expansion of g[i][k][!j].
C[i][j][k] = 1/2 (g[i][k][!j] + g[j][k][!i] - g[i][j][!k])
C[k][j][i] = 1/2 (g[k][i][!j] + g[j][i][!k] - g[k][j][!i])
Sum: = g[i][k][!j]
Lemma 2: To calculate g'[m][j][!k], from the metric inverse:
g[i][m] g'[m][j] = (i==j)
g[i][m][k!] g'[m][j] + g[i][m] g'[m][j][!k] = 0
g'[m][j][!k] = - g'[m][n] g[n][p][!k] g'[p][j] (m->p in the last sum)
= - g'[m][n] C[n][k][p] g'[p][j] - g'[m][n] C[p][k][n] g'[p][j]
Now let's compute the commutated second covariant derivative of a 1-form:
A[i][/j] = A[i][!j] - A[m] g'[m][n] C[i][j][n] (first deriv.)
A[i][/j][/k] - A[i][/k][/j] = (. = cancels)
A[i][!j][!k]. - A[m][!k] g'[m][n] C[i][j][n].
- A[m] g'[m][n][!k] C[i][j][n]
- A[m] g'[m][n] C[i][j][n][!k]
- A[m][!j] g'[m][n] C[i][k][n].
+ A[m] g'[m][n] C[p][j][n] g'[p][q] C[i][k][q]
- A[i][!m] g'[m][n] C[j][k][n].
+ A[m] g'[m][n] C[i][p][n] g'[p][q] C[j][k][q].
-A[i][!k][!j].+ A[m][!j] g'[m][n] C[i][k][n].
+ A[m] g'[m][n][!j] C[i][j][n]
+ A[m] g'[m][n] C[i][k][n][!j]
+ A[m][!k] g'[m][n] C[i][j][n].
- A[m] g'[m][n] C[p][k][n] g'[p][q] C[i][j][q]
+ A[i][!m] g'[m][n] C[k][j][n].
- A[m] g'[m][n] C[i][p][n] g'[p][q] C[k][j][q].
= A[m] g'[m][n] (- C[i][j][n][!k] + C[i][k][n][!j]
+ C[p][j][n] g'[p][q] C[i][k][q] - C[p][k][n] g'[p][q] C[i][j][q]
+ g[n][p][k!] g'[p][q] C[i][j][q] - g[n][p][j!] g'[p][q] C[i][j][q])
Using the lemma the g[n][p][k!] term combines with -C[p][k][n] giving C[n][k][p] and similarly for j!.
= A[m] g'[m][n] (- C[i][j][n][!k] + C[i][k][n][!j]
+ C[n][k][p] g'[p][q] C[i][j][q] - C[n][j][p] g'[p][q] C[i][k][q])
= - A[m] g'[m][n] R[n][i][k][j]
(meeting up with the standard definition of R, the Riemann-Christoffel tensor.) Now collect terms, remembering that g[m][n][/k] = 0:
g'[m][n] R[n][i][k][j] =
+ g'[m][n][!k] C[i][j][n]
+ g'[m][n] C[i][j][n][!k]
- g'[m][n] C[p][j][n] g'[p][q] C[i][k][q]
- g'[m][n][!j] C[i][j][n]
- g'[m][n] C[i][k][n][!j]
+ g'[m][n] C[p][k][n] g'[p][q] C[i][j][q]
= (g'[m][n] C[i][j][n])[/k] - (g'[m][n] C[i][k][n])[/j]
Get rid of the contraction with g'[m][n] leaving just the Riemann-Christoffel tensor:
R[L][i][k][j] = C[i][j][L][/k] - C[i][k][L][/j]
R[i][j][k][L] = C[j][L][i][/k] - C[j][k][i][/L] (L->i, i->j, k->k, j->L)
(It being understood that C does not transform as a tensor.) It's a curious fact that in 2 or 3 dimensions the covariant corrections all cancel out, but it's not likely so convenient in higher dimensions.
Now let's substitute the definition of C[...] in terms of the distance function:
R[i][j][k][L] = 0.5(r2[2/j][1/i][2/L][/k] - r2[2/j][1/i][2/k][/L])
(Expand [/k] as [1/k] + [2/k] since x2 == x1:)
R[i][j][k][L] = 0.5(r2[2/j][1/i][2/L][1/k] + r2[2/j][1/i][2/L][2/k]
- r2[2/j][1/i][2/k][1/L] - r2[2/j][1/i][2/k][2/L])
= 0.5(r2[2/j][1/i][2/L][1/k] - r2[2/j][1/i][2/k][1/L])
= g(x2,x1)[j][i][2/L][1/k] - g(x2,x1)[j][i][2/k][1/L]
(with the restriction that x2 == x1.)
Some important coordinate-related symmetries can be seen from the expression involving 0.5 r2:
R[i][j][k][L] = -R[j][i][k][L] = -R[i][j][L][k] = R[k][L][i][j]
since r2[2/i] = -r2[1/i] if x2 == x1.
In terms of the exterior derivative,
R[i][j][k][L] = C[j][L][i][/k] - C[j][k][i][/L] (L->i, i->j, k->k, j->L)
R[i][j] = dC[j]..[i]
where C[j]..[i] means the matrix-valued 1-form C[j][m][i] dx[m]. After differentiation and subtraction it is seen that the value is a matrix-valued 2-form.
Formula for the Christoffel Symbols
We would like to use the above expression for N to produce a formula for the Christoffel symbols in terms of distance function derivatives. Suppose q(x) is a field of vectors in a neighborhood of x1. Parametrize x2 along the geodesic by u and let p = q(x2(0)) = q(x1). The covariant derivative of the vector field measures the vectors' deviation from parallelism, and is zero at x2 when the field is parallel at x2. The formula for this is:
0 = (q[j][2!i] + q[L] C[L][i][m] g'(x2,x2)[m][j]) h(x2)[i]
The Christoffel symbol of the first kind, normally notated [ij,k], will be referred to as C[i][j][k]. The second derivative by t of Q(t,u) is constant as u varies (it's zero), so it has a zero first derivative by u. From this fact the ordinary derivative of q can be found. (Since q*q is constant equal to p*p, its derivative is 0 and is not written out.)
0 = Q(t,u)[!t!t] = 2(q.g(x2,x2).q + p.g(x1,x1).p - 2 q.g(x2,x1).p)
0 = Q(t,u)[!t!t][!u] = Q(t,u)[!t!t][2!i]h(x2)[i]
= 2 (q[j][2!i] g(x2,x1)[j][k] p[k] + q[j] g(x2,x1)[j][k][2!i] p[k]) h(x2)[i]
= 2 (q[j][2!i] + q[L] g(x2,x1)[L][m][2!i] g'(x2,x1)[m][j])
g(x2,x1)[j][k] p[k] h(x2)[i]
Where in the last step g'(x2,x1) is the inverse as a matrix of g(x2,x1). This is true if and only if the parenthesized term is in the null space of g(x2,x1)[j][k] p[k], but taking it as zero (not just in the null space) reveals a formula for the Christoffel symbols in terms of derivatives of the distance function. Leave out g(x2,x1)[j][k] p[k], let x2 == x1, and compare with the formula for the covariant derivative:
0 = (q[j][2!i] + q[L] g(x2,x1)[L][m][2!i] g'(x2,x1)[m][j]) h(x2)[i]
0 = (q[j][2!i] + q[L] C[L][i][m] g'(x2,x2)[m][j]) h(x2)[i]
C[L][i][m] = g(x2,x1)[L][m][2!i] = -0.5 r2[2/L][1/m][2!i]
C[i][j][k] = g(x2,x1)[i][k][2!j] = -0.5 r2[2/i][1/k][2!j]
where in the last line the subscript letters are merely substituted to have their usual values.
Ricci's theorem: g[i][j][/k] == 0. Proof:
g[i][j][/k] = g[i][j][2/k] + g[i][j][1/k]
= 0.5(r2[2/i][1/j][2/k] + r2[2/i][1/j][1/k])
Because r2 is symmetric under an end-to-end interchange, then when x2 == x1, the two terms are equal and opposite. QED.
As mentioned before.One idea that has been actively pursued by Arkani-Hamed, Dimopoulos, and Dvali  is that the brane is immersed in space with d extra large but compact dimensions. If the d+4 dimensional fundamental Planck mass is M, then the effective four-dimensional Planck mass follows in terms of the compact volume Vd by an elementary argument from the Einstein-Hilbert action:
An alternative explanation of the weakness of gravity is thus not that the fundamental Planck mass is so big, but rather that the compact volume is big. This raises the exciting prospect that the fundamental Planck scale may be more readily accessible in accelerator experiments, or that the compact dimensions may be detected through experiments with microgravity. This Theory says both. As far as the individual particles are concerned the compact volume is both large and small. It is the large value that makes gravity a weak force. But, it is the small value that determines everything else about a particle. It is the large value that holds part of the answer to Omega. It is the small value that hides the Higgs' manifold.
Now in the original string theory of the 1D types the String or manifold could be dwelt with as a sheet with two end points. As such, the finite element method could be used to determine stress elements of the membrane. Simular methods can be used even in this 10D format. It was this latter application of Eigen Functions and modes that led to String Theory in the first place as an outcrop of SUSY under QM. For a fuller treatment of these functions in relation to QM try: http://physics.bc.edu/MSC/430/ODE_Quantum/ODE_Quantum.html
To get a handle and view some questions on Klien typology try:http://www.cbloom.com/physics/kaluza.html
A good treatment on higher dimensions can be found at:http://www.cbloom.com/physics/dimensions.html
To conclude this let me leave you with the following quote and a further thought. "String theory therefore, is rich enough to explain all fundamental laws of nature. [...] It seems nothing less than a miracle that, starting from some purely geometric arguments from a string, one is able to derive the entire progress of physics of the last 2 millennia" (KAKU 1994, p.158). One problem that remains with string theory is that it is not a true TOE in that at best it can only discribed the physical world in relation to origin and quantum states. A true TOE would have to go far beyond this in being able to discribe the Macrocosmos as well as the microcosmos. Part of that Macrocosmos is the field on consciousness. Perhaps there is some truth to the idea that since we can ask the questions and observe the universe that that universe must be preordered to produce such a fact.
For a good beginning reference for the laymen try:http://physics.about.com/gi/dynamic/offsite.htm?site=http%3A%2F%2Fsuperstringtheory.com%2Fbasics.html
This theory can also be utilized in an 11D version. Thus, maintaining the original idea of M-Theory.
An earlier verson of this theory in non M-Theory format is found at:http://mypage.direct.ca/c/christie/Wavicle.html
For a good explination of Hilbert space see:http://jcbmac.chem.brown.edu/baird/QuantumPDF/Tan_on_Hilbert_Space.html
HELICAL PATH WITHIN HELICAL SURFACE DEMANDS GUAGING AND SPECIAL RELATIVITY.
If Helical path of light is constant(demanded by relativity) for each radius from the Strings axis of spin, as in a non-accelerating reference frame,the EM component must be gauged itself from the spin axis, if not the resulting direction of
light would not be consistant with C=VR+U at any radius. Thus, relativity demands a Guage that conserves itself.
However, this leaves a puzzle as far a GR is concerned. In the absence of an attracting mass, the the axis of spin does not change. The above generated field would then be intrinsically flat. But since the above field is co-couplled to others, thus, generating an inter connected space-time manifold, the field is not isolated in any case either locally or globally. As such, the field remains intrinsically curved. Thus, GR is restored, even inspite of a different mass energy tensor gauging. Each sub-space and the resulting fusion would have their own value for Omega.
As such, the proof of SR is found in the light cone/EM field guaging. Proof of GR is found in the interconnection of all Strings within 10D manifold. Thus, in spite of a differnt mass energy density tensor guaging to derive these answers the fields remain the same. As such, this theory incorporates regular QM and GR into a unified field theory.
For something else along these same lines goto the links page and go to my other site. Check out the information on that sites OUT OF THIS WORLD PAGE.
It can also be noted that my theory does follow one thing normal String Theory has always implied when it comes to blackhole geometrodynamics. That being, since the String, by its vary nature, is not a point object. The concept of a true singulairity in physics must be modified and replaced with an area of space-time that would have an off the scale gravity field strength. But it would not be an area that formed a literal singular point in space-time itself. As such, it is my conjecture that blackholes would be composed of strings at their most basic fundamental vibration state. Namely, that of a graviton. As such, some of Hawkin's theory on blackhole radiation can be explained a bit further than his theory was able to take one. At least now one can deduce an answer to what happens to the other particle as it enters the blackhole.