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Join Date: Mar 2018 Location: Xinhui Guangdong Province China
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 X4 Model of Unit Electrical Charge
Declarations:
This X4 model of unit electrical charge is established in X4 theory and contains some guess of its own. Anybody shall not try to relate other similar theory to it.
The major purpose of this model is to explore the logical relationship between chirality, space and charge, anybody should just ignore it if he (or she) feel it inappropriate or incomplete.
X4 Model of Unit Electrical Charge
Let’s see the unit step function:
μ(t) = 0 (t＜0) μ(t) = 1 (t＞0)
It could be interpreted here as below:
Because t＜0 meaningless, so the signal or the state of matter does not exist.
When t＞0, the signal or the state of matter exist.
Next, play a mathematical game of anti..
With Fourier transformation (detailed calculation omitted), we got:
1 = (1/2) + (1/π)∫0→+∞（1/ω）sinωt dω
Then, replace variants, we got:
1 = (1/2) + (1/π)∫0→+∞（1/X）sinXP dX
Namely:
1 = (1/2) + (1/2) = (1/π)∫0→+∞（1/X）sinXP dX + (1/π)∫0→+∞（1/X）sinXP dX ①
And so on, we got:
1 = [(1/2) + (1/π)∫0→+∞（1/X）sinXP dX]
= (1/π)∫0→+∞（1/X）sin(X)P d(X）+ (1/π)∫0→+∞（1/X）sin(X)P d(X)
If we take X1 = X, then
1 = (1/2) + (1/2) = [(1/π)∫0→+∞（1/X1）sinX1P dX1] + [(1/π)∫0→+∞（1/X1）sinX1P dX1] ②
And so on, we got:
0 = (1/2) + (1/2) = (1/π)∫0→+∞（1/X）sinXP dX +[ (1/π)∫0→+∞（1/X1）sinX1P dX1 ] ③
Next, let’s analyze the characteristics of equation①②③
⑴ In macro, it’s a scalar constant.
⑵ In micro, it has something to do with space.
⑶ The value of the constant inverts follow suit the inversion of space. And there is a case of neutrality.
⑷ According to the replacement of variant, P＞0,and could be regarded as the length of momentum.
According to the integration area, X＞0, and could be regarded as the distance of space point to the origin of coordinate system.
And（1/X）sinXP could be regarded as the space part of a wave function in triangular form. If we see it wave function in momentum space, φ(P) =（1/X）sinXP , it represents a wave function distribution field adjacent to the origin of coordinate system.
And (1/π)∫0→+∞（1/X）sinXP dX represents the comprehensive result of the field.
And the situation of X1 is the same.
We see that equation①②③ are very similar in nature to one physical quantity, it’s electrical charge.
Next, we just use them as the mathematical model for unit electrical charge (+e or –e) and electrical neutrality and analyze them a further step. We got:
(A) Unit electrical charge has deeper cause in it. The deeper structure of matter could be called layer here. The electrical charge of such layer is + (1/2)e or  (1/2)e, simple equivalent to (1/π)∫0→+∞（1/X）sinXP dX or  (1/π)∫0→+∞（1/X1）sinX1P dX1. Value inverted follow suit the inversion of space.
(B) Because the two wave function distribution fields：
（1/X）sinXP and（1/X）sinXP in case of equation①,
（1/X1）sinX1P and（1/X1）sinX1P in case of equation②,
（1/X）sinXP and （1/X1）sinX1P in case of equation③,
Have the same origin of coordinate system in the respective case, and because only one direction is analyzed here, in fact, all direction should be the same situation,
So, the ideal Geometrical shape of layers in any case of equation①②③ should be concentric circle kind in any normal cutting plane of a sphere.
(C) Layers in any case of equation①②③ might be the two aspects of one thing naturally.
(D) We can’t exclude a very special case：there is a kind of layer which has no space inversion effect( namely 0 = 0 + 0). Of course, it will be electrical neutral.
Next, analyze what specific physical structure could realize the conditions mentioned above from (A) to (D).
We think about circle kind of electromagnetic standing wave in any normal cutting plane of a sphere.
It’s two aspects (two travelling waves go in opposite direction) of one thing (the standing wave).
And we got the important character of layer: layers which construct a basic particle could not be separated by means of collision. No alone layer exist in nature.
We check out the ordinary standing wave function:
Y =（2Acos2πx/λ）cos2πγt
It has no space inversion effect.
We consider the track of the standing wave:
If the track is a smooth circle, its shape is too simple. Look at a smooth circle in the XY plane. The parametric equation is :
X = r cosθ Y = r sinθ
If space inverted θ= θ1, then：
X = r cosθ1 Y =  r sinθ1
That’s another smooth circle in the XY plane which derived from reflection of the original circle against X axis. In fact, they are copy. No, space inversion effect. We put it aside temporarily.
If the track is a helical line, it has chirality（called natural identification of space here）.
Look at the parametric equation of a helical line:
X = r cosθ Y = r sinθ Z = kθ
If space inverted θ= θ1, then：
X = r cosθ1 Y =  r sinθ1 Z =  kθ1
The chirality inverted.
Then the specific physical forms of that circle kind standing wave could be:
(Ⅰ) Superposition of two right hand helical circle kind travelling waves go in opposite direction, namely, Superposition of two right hand layers.
(Ⅱ) Superposition of two left hand helical circle kind travelling waves go in opposite direction, namely, Superposition of two left hand layers.
(Ⅲ) Superposition of one right hand helical circle kind travelling wave and one left hand helical circle kind travelling wave go in opposite direction, namely, Superposition of one right hand and one left hand layers.
If we artificially define situation(Ⅰ) as basic particle with positive unit electrical charge, then, situation (Ⅱ) would be basic anti particle with negative unit electrical charge. Situation(Ⅲ) would be basic neutral particle with electrical neutrality.
Now, consider the track of a smooth circle mentioned above again. It would be:
(Ⅳ) Superposition of two circular travelling waves go in opposite direction, namely, Superposition of two neutral layers. It would also be basic neutral particle with electrical neutrality.
At this moment, we can talk about the micro standard for the determination of some X4 states:
If we define basic particle made up of two right hand layers as in the state of X4 = +1, then, basic particle made up of two left hand layers will be in the state of X4 = 1, namely, the anti particle. Basic particle made up of one right hand layer and one left hand layer will be in the superposition states of
X4 = +1 and X4 = 1. Basic particle made up of two neutral layers is in the state of X4 = +1 or X4 = 1, which means its anti state is itself.
And so on, the micro standard principle is also applicable to the determination of the states of X4 = 2,3,4,5……n and their counter part X4 =  2,3,4,5……n.
Watch the context in counter way, it appears that the chirality of layer determines space. Inversion of
the chirality of layer leads to the inversion of space. Inversion of space leads to the inversion of unit electrical charge.
Note:
Maybe, equation①②③ is not necessarily the accurateenough equations to describe the real wave function distribution fields of basic particles, but it still can demonstrate some and has no contradiction to facts:
1. Under such a model, unit electrical (charge) interaction between basic particles will be just the determination of probability method of existence each other, and only has something to do with distance (∝1/X).
2.Since the value of P does not affect the result of integration in equation①②③, that means the relative motion of basic particles do not affect the volume of unit electrical charge.
Chen Li Qiang
July, 2018
Additions:
Below are some predictions based on the above article:
1. When the circle kind standing wave mentioned in the above context broken, it will transform into a kind of released photon. So, the flying track of leased photon in flat space should have three types: straight line, straight right hand helical line, straight left hand helical line.
2. In micro, the anti photon of a released photon is itself in case of straight line track. But in case of straight helical track, the anti photon of a released photon is its counter part with inverted chirality. In macro, namely, in respect of spacetime effect, they are all the same and in the state of X4 =∞.
Chen Li Qiang
July, 2018
