ele-mental ugliness

AntonioLao · **ele-mental ugliness -** 04-09-2006, 03:15 PM

About forty years ago the matrix notation for the imaginary unit $\sqrt{-1}$ was first noted in a thin booklet on the shelve cataloged under the Dewey system at the local public library in Cebu City, Philippines. The second opportunity of seeing it was as late as the morning of April 7, 2006 at the book shelves of one of City of Plano public libraries. The book is volume 1 of Fundamentals of Mathematics, edited by H. Behnke, F. Bachmann, K. Fladt, and W. Süss, and translated by from the second German edition of 1962 by S. H. Gould, chapter 8, page 460. This second sighting is hoped to end the search for a justification of finally completing the circle marking a return to exclusive use of real numbers for TOE and placing the complex number field on the reserved sideline of all mathematical analyses.

In matrix notation the imaginary unity is defined as $i=\sqrt{-1}=\left(\begin{array}{cc}0&1\\-1&0\end{array}\right)$ . This allows complex numbers a + ib to be written as
$\left(\begin{array}{cc}a&b\\-b&a\end{array}\right)=\left(\begin{array}{cc}a&0\\0&a\end{array}\right)+\left(\begin{array}{cc}0&1\\-1&0\end{array}\right)\left(\begin{array}{cc}b&0\\0&b\end{array}\right)$
The determinant c = a + b is called the norm. This is purely an algebraic definition which gives the only existential property of real numbers as a + b ≠ 0 if and only if a ≠ 0 or b ≠ 0, consequently justifying the existence of a complex field. Its discovery since 1500s have been applied in mathematical and physical sciences, from the search for a theory of prime numbers to electromagnetism, special relativity, quantum mechanics, quantum field theories, and to general relativity. All imply some descriptive mechanism of singular rotational transformation. And in 1949, Gödel theorized the existence of large-scale rotational vortex for the singular universe of positive energy for a positive vacuum field.

The ugliness lies in the positions of the elements of negative and positive unity. These show an inherent asymmetry and the condition that pure rotation exists if and only if a + b = 1 with degenerate solutions of a = b = Ö2/2. Although the use of complex components spinors in Dirac’s theory explains precisely the existence of magnetic moment, it shorts of explaining why this exists at all, for to attempt an explanation is no more than to hypothesize the existence of double infinitesimal rotations and taking the universe as a whole the total sum of these add to zero. This justifies the observed homogeneity and isotropy and disproving Gödel’s theory of large-scale vortices and large-scale time reversal but not small-scale time reversal. The proof of infinitesimal time reversal is contained in Feynman’s theory of the positrons. See Physical Review, Vol. 76, p 749 (April 8, 1949).

baudrunner · 04-09-2006, 06:48 PM

I would like better an explanation for why when I bold c = a + b it comes out c = a + b which results in a completely different mathematical conclusion.

mkirkpatrick · 04-09-2006, 06:59 PM

Quote:

Originally Posted by AntonioLao

About forty years ago the matrix notation for the imaginary unit

was first noted in a thin booklet on the shelve cataloged under the Dewey system at the local public library in Cebu City, Philippines. The second opportunity of seeing it was as late as the morning of April 7, 2006 at the book shelves of one of City of Plano public libraries. The book is volume 1 of Fundamentals of Mathematics, edited by H. Behnke, F. Bachmann, K. Fladt, and W. Süss, and translated by from the second German edition of 1962 by S. H. Gould, chapter 8, page 460. This second sighting is hoped to end the search for a justification of finally completing the circle marking a return to exclusive use of real numbers for TOE and placing the complex number field on the reserved sideline of all mathematical analyses.

In matrix notation the imaginary unity is defined as

. This allows complex numbers a + ib to be written as

The determinant c = a + b is called the norm. This is purely an algebraic definition which gives the only existential property of real numbers as a + b ≠ 0 if and only if a ≠ 0 or b ≠ 0, consequently justifying the existence of a complex field. Its discovery since 1500s have been applied in mathematical and physical sciences, from the search for a theory of prime numbers to electromagnetism, special relativity, quantum mechanics, quantum field theories, and to general relativity. All imply some descriptive mechanism of singular rotational transformation. And in 1949, Gödel theorized the existence of large-scale rotational vortex for the singular universe of positive energy for a positive vacuum field.

The ugliness lies in the positions of the elements of negative and positive unity. These show an inherent asymmetry and the condition that pure rotation exists if and only if a + b = 1 with degenerate solutions of a = b = Ö2/2. Although the use of complex components spinors in Dirac’s theory explains precisely the existence of magnetic moment, it shorts of explaining why this exists at all, for to attempt an explanation is no more than to hypothesize the existence of double infinitesimal rotations and taking the universe as a whole the total sum of these add to zero. This justifies the observed homogeneity and isotropy and disproving Gödel’s theory of large-scale vortices and large-scale time reversal but not small-scale time reversal. The proof of infinitesimal time reversal is contained in Feynman’s theory of the positrons. See Physical Review, Vol. 76, p 749 (April 8, 1949).

Antonio,What I seem to be seeing here is a possible way of expressing the
consciousness is the keyto the toe theory?What do you think!
regards michael.

Mohan.C · 04-10-2006, 11:40 AM

What is amp;?

AntonioLao · 04-10-2006, 12:48 PM

Quote:

Originally Posted by Mohan.C

What is amp;?

They should not be there. All these must be taken out for the matrix to make any sense. There is still some problems with the latex. Will fix it asap.

Quote:

Originally Posted by mkirkpatrick

What I seem to be seeing here is a possible way of expressing the consciousness is the keyto the toe theory?

I still need to post the symmetric Hadamard matrices as quanta of spacetime. Since consciousness of part of spacetime, it make sense to describe it as matrices.

Quote:

Originally Posted by baudrunner

it comes out c = a + b which results in a completely different mathematical conclusion.

This a problem with the text editor. If unbold it looks back ok.

AntonioLao · **time reversal -** 04-10-2006, 02:13 PM

I am trying to get hold of a copy of Gödel’s paper “An Example of a New Type of Cosmological Solution of Einstein’s Field Equations of Gravitation,” Rev. Mod. Phys. 21, 447 (1949). This paper indicated that time reversal is possible.

mkirkpatrick · **it is there in the mist,and the sun is rising? -** 04-10-2006, 08:09 PM

Antonio,I have a gut feeling that you are on to something that will be quite
profound,and that from this matrice,there will come a radiant beam that will
cast a net outwards,and when we all haul it back in,there inside will be the
answer that can be expressed as the t.o.e.!You can do it Antonio!May the
force be with you?

kind regards michael.

Lloyd Gillespie · **Godel and Einstein... -** 04-12-2006, 08:42 PM

Quote:

Originally Posted by AntonioLao

I am trying to get hold of a copy of Gödel’s paper “An Example of a New Type of Cosmological Solution of Einstein’s Field Equations of Gravitation,” Rev. Mod. Phys. 21, 447 (1949). This paper indicated that time reversal is possible.

Antonio, could you please give me a shout by private message if you find this paper, or where it is located on the web?

Regards,
Lloyd

AntonioLao · 04-13-2006, 11:54 AM

Quote:

Originally Posted by Lloyd Gillespie

could you please give me a shout by private message if you find this paper, or where it is located on the web?

I can't find a free copy but for $50 you can purchase it at http://prola.aps.org/abstract/RMP/v21/i3/p447_1