# Quantized Space (H)

1. Jan 9, 2004

### Antonio Lao

Quantized space H can only exist in one dimension. Its equation is given by equation 1-1, the square of the total energy of the universe. The units of quantized space are the two distinct space charges, H+ and H-. For LOE order 2, their matrix representations are the following:

$$H+=\left[\begin{array}{cc}+1&-1\\-1&+1\end{array}\right]$$ and $$H-=\left[\begin{array}{cc}-1&+1\\+1&-1\end{array}\right]$$

For LOE order of zero, the representation is a cube. Where the vertices have alternating value of 1 and –1. For LOE order of 1, they are [1] and [-1]. The H’s only represent one side of this cube. There are six sides. If the cube has a total space charge of one unit, then the space charge of H+ is 1/6 and the space charge of H- is -1/6. The procedure of adding space charges is the same as matrix addition. The procedure for multiplication of space charges is the same as matrix multiplication with one exception that the commutative rule always holds. The interactions of space charges are calculated by matrix multiplication. The identity element, under the operation of addition of space charges, is given by H0. It has the following properties:

1. [H0]+[H0] = H0
2. [H+]+[H-] = H0
3. [H+]+[H0] = H+
4. [H-]+[H0] = H-

Property 2 indicates that the inverse of H+ is H- and conversely, the inverse of H- is H+. where H0 is the 2 by 2 matirx with all elements equal to zero. For LOE order 2, [H0] is given by the null matrix:

$$H^0=\left[\begin{array}{cc}0&0\\0&0\end{array}\right]$$

The table for addition of the group of H+, H- and H0 is given as the following

+ H0 H+ H-
H0 H0 H+ H-
H+ H+ 2H+ H0
H- H- H0 2H-

The binary operations for multiplication of H+, H- and H0 are the followings:

[H0][H0] = H0
[H+][H0] = H0
[H-][H0] = H0
[H+][H-] = 2H-
[H-][H+] = 2H-
[H-][H-] = 2H+
[H+][H+] = 2H+.

The multiplication table is given by the following:

x H0 H+ H-
H0 H0 H0 H0
H+ H0 2H+ 2H-
H- H0 2H- 2H+

It can be noted that the null row and column can be deleted to give a simplified table given as

x H+ H-
H+ 2H+ 2H-
H- 2H- 2H+