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Science Forum Index » Physics Forum » Quantum Gravity 282.93: Taiwan and Japan Discover the...
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| OsherD... |
 Posted: Fri Jul 11, 2008 6:00 pm |
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From Osher Doctorow
Toshihiro Matsuo, Dan Tomino, Wen-Yu We, and Syoji Zeze, 1st 2 of U.
Tsukuba Japan, 3rd National Taiwan Normal U. Taiwan, 4th National
Taiwan U. Taiwan, in "Quantum gravity equation in large N Yang-Mills
quantum mechanics," arXiv: 0807.1186 v1 [hep-th] 8 July 2008, 21
pages, regard the Schrodinger equation in BFSS large N matrix
mechanics as the Wheeler Dewitt equation which determines the wave
function of the Univers and get an explicit solution of the wave
function which they study in a simple 2-dimensional minisuperspace
model having form of the square root of a function involve t^(-5/3)
and y^(-3) in a toy model of the Universe given by:
1) ds^2 = dt^2 + (1/y(t)^2)dx^2 (2-dimensional version of Robertson-
Walker Universe)
We can examine the Probable Causation/Influence (PI) relationships of
Cubic arguments by looking at:
2) x^3 + y^3 = (x + y)(x^2 - xy + y^2)
so that:
3) [x^3 + y^3]/(x + y) = x^2 - xy + y^2 = (x^2 o y^2) - xy + x^2y^2 =
(x^2 o y^2) - xy(1 - xy) = (x^2 o y^2) - Logistic(xy) (where x o y =
x + y - xy is Jacobson Radical star product)
and solving for Logistic(xy) which equals xy(1 - xy) yields:
4) Logistic(xy) = (x^2 o y^2) - [x^3 + y^3]/(x + y)
So the Logistic type function Logistic(x) = x(1 - x) when it has
argument xy decomposes into a Jacobson Radical star product of x^2 and
y^2 and a cubic in x and in y divided by x + y (linear), that is to
say 1st, 2nd, and 3rd powers of x and of y. Likewise, solving (4) for
the cubic gives the cubic as a function of Logistic(xy) and x^2 o y^2
and x + y, that is to say multiplication of x and y, addition of x and
y, and star product of their squares, which is certainly "recursive"
at least in the degrees of the variables.
Osher Doctorow |
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