axis and pole

[AntonioLao]

The elementary particle belonging to the family of leptons called the electron exhibits both polar and axial properties of vectors. Its polarity comes from the attribute of electric charge while its axiality comes from the attribute of intrinsic angular momentum usually called the spin in quantum mechanics. For the electrons, both properties are quantized. Why? It is still a mystery. Furthermore, both properties are relativistic invariance. That is to say increasing the linear velocity does increase or decrease their values. On the other hand, the mass property of electrons is a continuous function of its velocity (linear or angular). Therefore, the mass is not a relativistic invariance. Nonetheless, charge, spin, and mass made the electron what it is in comparison to other elementary particles.

The truth of the matter is there are no physical theories that directly derived charge and spin, charge and mass, or spin and mass from each other although all three give certain information about the quantized energy states of the electrons. This positively indicates that for electron the rule of quantum category is truly upheld. That is to say natural transformations only exist for an object’s properties of the same type: pole to pole, axis to axis. In the functional domain, even to even, odd to odd, for example the circular complementary trigonometric functions of sine and cosine. Their infinite series expansions are the following: sin(x)=x-x/3!+x/5!-…or - and cos(x)=1-x/2!+x/4!-… or - . Note that n is always odd for sine and always even for cosine. Moreover, the conjugates of complex numbers, superposition of wavefunctions are all quantum categories of the same type. Fortunately, the vector product of two polar vectors is an axial vector. This mathematical fact can help formulate a quantum theory of the space-time continuum as squares of energy using binary operations of categorized symmetric Hadamard matrices given minimum order 2 as and.

[SB_UK]

This mathematical fact can help formulate a quantum theory of the space-time continuum as squares of energy using binary operations of categorized symmetric Hadamard matrices given minimum order 2 as and.

http://en.wikipedia.org/wiki/Pitch_(music)

2 4 8 16 32 64 128 [Middle C 256Hz]

http://en.wikipedia.org/wiki/Hadamard_matrix

In mathematics, a Hadamard matrix is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal.In geometric terms, this means that every two different rows in a Hadamard matrix represent two perpendicular vectors ... ...

1 -3
|
2

1 ^3
(
2

1 ^3
(
2

or

1 n3
v

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1 ()3
|
v


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1 ()3
|
v

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vn -> 1d wavelength of convex and concave component

- representing linear and circular motion

---------
\----/\\\\
-\--/-\\\\\
--\/--\\\\\\

- hard to imagine anything simpler than a 1d standing wave as the basis to reality.
It changes, gives us a duality -
evolves through its point of inflexion (trinity).

We have polarity - the maxima and minima, axial - the linear direction of blue and spin state -
pink rotating 'on the spot'.

The 3 dimensions come from the plane of pink (2) + 1 from blue.

Two balls side by side -
oo

- the ball on the left rotates towards us (though holds its position) - on a plane
- the pink ball rotates clockwise (to the right) -
though holds its position - on a plane.
y
|//z
|/
----x

zy xy duality,wave,sphere rotation,inter-dependence,evolution by Hadamargy-bargy


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1 ()3
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v

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vn