Matter vs anti matter

In X4 Theory, one factor “X4” is employed to denote the matter state, or say “the inherent property” of particle. If the positive X4 value represents “particle”, then the negative X4 value represents “anti - particle”.
The inversion of space, time, and charge is decided by the inversion of X4 value.
(The primary concept of X4 Theory could be found in the thread “Can projective geometry find out its application in physics?” in the geometry column.)
他江门地方黑恶势力钟永康集团及新会一中九一四班姓蔡的万岁，万岁，万万岁！当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Liqiang Chen 陈力强
Oct 11, 2020

I point out in the chapter The Basic Mechanics for Anti Matter that the four dimensional space of an anti particle is inverted: X’ = - X = - x
People might imagine that time t could be inverted too, and the symbols – t or d (-t) appeared in some lecture books. They seem meaningful to describe anti matter in math, but they are meaningless to describe anti matter in physics (or this real cosmos). I will interpret why in X4 theory of time.
Now, let’s turn to the negative energy state about particle in the chapter Klein - Gordon equation in Relativistic QM. The wave function for such situation of free particle could be seen:
Ψ（x, t）= N exp( -i(Et – p•x)) E＜0
How it is reinterpreted with – t and d (-t), see those lecture books. Next, I reinterpret it in X4 theory.
Ψ（x, t）= N exp( -i( - |E|t – p•x))
= N exp( i( |E|t + p•x))
= N exp( i( |E|t – p•（- x))）
= N exp( i( |E|t – p•（-X))）
So:
Ψ（X’, t）= N exp( i( |E|t – p’•X’)), (Note: three dimensional space momentum p = p’)
And we notice that the above representation is equivalent to
Ψ（X’, t）= N exp( i(p’•X’– |E|t ))
= N exp(- i(|E|t– p’•X’))
The reinterpretation of the above wave function is: positive energy anti particle flows forward in time in its four dimensional space.

Next, make a further step transformation:
= N exp(- i(|E|t– (- p’ )•(-X’)))

= N exp(- i(|E|t+ p•X))
It means the probability wave for a particle flying backward is the same with the anti probability wave for its anti particle flying forward.

Regardless the topic of negative energy state, it’s important to see the four dimension spacial method of representation of probability wave.
For a free particle, it is:
Ψ（X, t）= N exp(- i(Et– p•X))
For the corresponding anti particle, it is:
Ψ（X’, t）= N exp(- i(Et– p’•X’))
E > 0

Pay attention please, p and p’ are three dimension spacial momentum while X and X’ are four dimension space. So they are both four dimension spacial wave functions.

X4 Model of Unit Electrical Charge

When we watch a spiral spring, we find that the chirality, left handed or right handed, is natural spacial property and will not change following movement / reference frames.
The concept of dimension should be continues and integral. Why this kind of natural spacial property seems to disappear down to microscopic scale? One solution might be that it reflects in the structure of basic particles.
Another question is that if a unified property existing in nature to judge “anti”, including charges?
A nonstandard model is initiated here in X4 Theory and have a try to solve these problems.
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/R）sinR p dR
Namely:
1 = (1/2) + (1/2) = (1/π)∫0→+∞（1/R）sinR p dR + (1/π)∫0→+∞（1/R）sinR p dR ①
And so on, we got:
-1 = -[(1/2) + (1/π)∫0→+∞（1/R）sinR p dR]
= (-1/2) + (-1/2) = (1/π)∫0→+∞（1/-R）sin(-R) p d(-R）+ (1/π)∫0→+∞（1/-R）sin(-R) p d(-R)
If we take R’ = -R, then
-1 = (-1/2) + (-1/2) = [(1/π)∫0→-∞（1/R’）sinR’ p dR’] + [(1/π)∫0→-∞（1/R’）sinR’ p dR’]
= [-(1/π)∫0→+∞（1/R’）sinR’ p dR’] + [-(1/π)∫0→+∞（1/R’）sinR’ p dR’] ②
And so on, we got:
0 = (1/2) + (-1/2) = (1/π)∫0→+∞（1/R）sinR p dR +[- (1/π)∫0→+∞（1/R’）sinR’ p dR’ ] ③
Note: in the final result of equation②, the value of R’ is positive too because it has changed to be in the anti 4D space. The equation of R’ = -R just reflects the contrast relationship of two contrast 4D spaces.

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 R.
⑶ The value of the constant inverts following the inversion of the four dimensional space. And there is a case of neutrality.
⑷ According to the replacement of variant, p ＞0,and could be regarded as the magnitude of three dimension spacial momentum.
According to the integration area, R ＞0, and could be regarded as the four dimension space for a particle R = X4 r, X4> 0, r > 0, r is the distance (3D space) from the origin of the coordinate system.
And（1/R）sinR p could be regarded as the space part of a position space wave function in triangular form in 4D space. If we apply wave function in momentum space in 4D space, it will beΨ(P ) =（1/r）sinr P , it represents a wave function distribution field adjacent to the origin of coordinate system. The property of this field is not even. It ∝1/r. When the distance trends to infinite, the field trends to zero. While the distance trends to zero, the field trends to infinite.
And (1/π)∫0→+∞（1/r）sinr Pdr represents the comprehensive result of the field.
The situation of R’ could be regarded similar but for an anti particle.
We see that equation①②③ are very similar in nature to one physical quantity, it’s point 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/R）sinR p dR or -(1/π)∫0→+∞（1/R’）sinR’ p dR’. Value inverted following the inversion of the four dimensional space R.
(B) Because the two wave function distribution fields：
（1/R）sinR p and（1/R）sinR p in case of equation①,
（1/R’）sinR’ p and（1/R’）sinR’ p in case of equation②,
（1/R）sinR p and （1/R’）sinR’ p 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: No alone layer exists in nature. Layers which construct a basic particle could not be separated by means of collision. There seems to be a strong force constraining that two lays but in fact that strong force is just a false impression.

We check out the ordinary standing wave function:
Y =（2Acos2πx/λ）cos2πγt
It’s an even function and 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 Z = 0
If space inverted θ= -θ’ then：
X = r cosθ’ Y = - r sinθ’ Z = 0
That’s another smooth circle in the XY plane which derived from reflection of the original circle against X axis and in fact is the copy. No space inversion effect too. We put it aside temporarily.

If the track is a helical line, it has chirality, left handed or right handed（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= -θ’ then：
X = r cosθ’ Y = - r sinθ’ Z = - kθ’

The chirality inverted.
Then the specific physical forms of that circle kind standing wave could be:
(Ⅰ) Superposition of two right handed helical circle kind travelling waves go in opposite direction, namely, Superposition of two right handed layers.
(Ⅱ) Superposition of two left handed helical circle kind travelling waves go in opposite direction, namely, Superposition of two left handed layers.
(Ⅲ) Superposition of one right handed helical circle kind travelling wave and one left handed helical circle kind travelling wave go in opposite direction, namely, Superposition of one right handed and one left handed 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. Namely, “anti” is just relative. 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 handed layers as in the state of X4 = +1, then, basic particle made up of two left handed layers will be in the state of X4 = -1, namely, the anti particle. Namely, “anti” is just relative. Basic particle made up of one right handed layer and one left handed 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.
The micro standard is also applicable for the determination of the X4 states of the layer 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.
So, if we define proton “particle”, then electron actually is a kind of “anti particle”, while positron is a kind of “particle”.

Watch the context in counter way, it appears that the chirality of layer determines the contrary of four dimensional space. Inversion of the chirality of layer leads to the inversion of four dimensional space. Inversion of four dimensional space leads to the inversion of unit electrical charge.

Note:
Maybe, equation①②③ is not necessarily the accurate-enough equations to describe the real wave function distribution fields of basic particles, but it still can demonstrate some properties 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 or say∝|1/x|²= 1/x²).
2.Since the value of three dimension spacial momentum 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.
3. Charge conservation, because 4D space is naturally symmetric.
他江门地方黑恶势力钟永康集团及新会一中九一四班姓蔡的万岁，万岁，万万岁！当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Piggy now knows how to insert diagram for better understanding of the theory. Below is a picture of spiral spring which demostrates the natural spacial property.

............................................
Note: Actually the elementary particle model in X4 Theory should be a spherical surface. But for intuition sake, the “circle kind standing wave” can serve as a simplified model. And for convenience in calculation in chapters below, the simplified model is applied. And it’s considered that the energy on the spherical surface be converted entirely into the “circle kind standing wave”.

Liqiang Chen
Oct 20, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Should piggy surrender to the First Order (the local dark lords of the Jiangmen city)?
他江门地方黑恶势力钟永康集团及新会一中九一四班姓蔡的万岁，万岁，万万岁！当今时代，全世界没有什么人能够值得如此殊荣。呵呵

A big part of science is conjecture, which means making up "What if" scenarios. Often those scenarios get discussed a lot for a long time, and people begin to assume they are true just because they keep hearing them.

Unfortunately there is no flag to indicate that a person is offering a conjecture, not actual knowledge. It's even worse when they conjecture about things that have not even been observed.

“A big part of science is conjecture,”
No bad a comment. In this sense, the most famous parable might be “touching the elephant”. Unfortunately there is a “standard model” get discussed a lot for a long time, and people begin to assume they are true just because they keep hearing them. Science should encourage alternative method / angle of touching besides the “standard” method.
In respect of research in the territory of anti matter, piggy would rather trust in natural philosophy (the natural spacial property of spiral spring, how to identify what’s male rabbit and what’s female rabbit, etc) which can be observed than such conjecture as “to see Einstein”. If the starting point of a conjecture is inappropriate in philosophy, no matter how complicated it will be, it’s a game (in math). That’s why piggy start this thread in philosophy forum rather than the physics forum.

“What if ” scenarios are common methods in physics research. The key point is to see that “What if ” scenario can solve what physics / astronomical phenomena in ONE way. If it can do well, that means he didn’t miss the target of the elephant.
他江门地方黑恶势力钟永康集团及新会一中九一四班姓蔡的万岁，万岁，万万岁！当今时代，全世界没有什么人能够值得如此殊荣。呵呵

In this post, piggy wants to talk about an example in QM which “get discussed a lot for a long time, and people begin to assume they are true just because they keep hearing them.” It’s the conception of “matter wave”. (Although it’s not directly relevant to the theme of this thread, it could be considered as the extension of the topic on going.)

The diffraction pattern of electron is about below:
The electrons emitted one by one, poop, poop, poop…passes through a slit…then, a tiny point appears in this place or that place randomly on the screen/film. Time long enough, the diffraction pattern of electron appears on the screen/film.
Conclusion: It is the presentation of wave character of electron.
This piggy thinks that the randomly shooting is the behavior of wave character. But what’s tiny point on the screen/film? If it’s not a particle, what’s it?
So, in all around consideration, the conclusion should be: It’s the presentation of wavicle character of electron.
The “wave character” is of course the “probability wave” in math. But what kind of wave is it in physics? The current “standard” answer is the “matter wave”. Actually, the electron moves in electric field in the apparatus. So, how can people assure that the “matter wave” is the “probability wave”? It seems conjecture in logic, because there might be another possibility that it's due to the electric filed has wave characteristic too.

When it comes to double slits, situation might be more complicated.
When talking about the double slits experiment for electron, the current “standard” explanation is “all possible paths” which means one electron can passes through two slits (piggy often jokes “one rabbit in two holes”). Piggy heard one genius (Toppy Sir) said in PHF that “how lame it all sounds…” Piggy likes to laugh at such guy: if you feel it lame, why not try to explore it in an alternative way and see if you can understand it in a better way?
Actually the electron moves in electric field in the apparatus.
Electric field can be in two holes while the rabbit just can be in one hole. It’s understandable thing.
Why we must pursue such theory as “one rabbit in two holes” which we can’t understand.
(So, why must we use one electron can passes through two slits to explain the interference pattern?)

Moreover, the property of objective existence of matter in cosmos should not change following observation by human.
……………………………………………………..

Actually, the X4 unit charge model demonstrates that electric interaction has an aspect of wave characteristic.
A special situation in GR (without gravity) is SR. How about electric interaction? When electric interaction disappears, it’s a free particle. An ideal situation of this is the infinite distance. We can see that the amplitude 1 / r of the wave function Ψ(P ) =（1/r）sinr P in the X4 unit charge model trends to zero when distance r trends to infinite. Actually the wave function will no longer meaningful. How to maintain the uniform of representation in math? We can assume the amplitude of the wave function is a constant A and it means the situation of without electric interaction. That’s the wave function for free particle.
Of course, in X4 Theory, when the situation of without electric interaction happens, no need resorting to wave function. The factor X4 itself represents the equal probability effect. It reflects the uncertain property (contrast of ability) of the free particle itself.

Liqiang Chen
Nov 3, 2020
给他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁一个超文革赛阎王光荣称号快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

X4 Explanation of Double Slits Experiment for Electron

Because the wave function for free particle is just a mathematical form while the physical meaning of wave already lost, the application of it to explain the generation of interference pattern in the double slits experiment of electron is inappropriate (e.g. “all possible paths, interference with itself, etc”).
An alternative method to explain it is as below:
Actually the electron moves in electric field in the apparatus.
The electron passes through either one of the slits. No matter which slit the electron passes through, the wave characteristic of electric interaction will cause interference information in the slits.
When electro - magnetic detector(s) fixed to observe, those interference information created in the slits will be disturbed by the physical interaction between electron and detector(s), and then the interference pattern will disappear.
The principle is also applicable to explain the diffraction pattern in the single slit experiment for electron.

Liqiang Chen
Nov 3, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班姓蔡的万岁，万岁，万万岁！当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Philosophy of the energy – mass relationship:

We know that, in SR, Einstein derived the relationship of energy - mass c².

Below, we explore from another angle using another theory and see if we can get it.
Construct a model of spherical electromagnetic wave: circle kind of standing electromagnetic wave on any normal cutting plane of the small sphere. (You can imagine the sea waves in the Pacific, Atlantic and Indian Oceans…Of course, this imagination is just for easy to understand the conception of the spherical model). Then, the energy of the electromagnetic wave is confined on the small spherical surface (deposited) and will not demonstrate the property of energy. X4 Theory considers this spherical model as a model of elementary particle. It demonstrates the property of mass only.
Next, unfold the circle kind of standing electromagnetic wave on any normal cutting plane of the small spherical surface. It travels in straight line in a speed of c. X4 Theory considers it as the physical model of a released photon. The property of energy can be demonstrated.
Because it’s just that thing, what different is just the moving speed of c in straight line. Then, the relationship between the energy of the released photon and the mass of the circle kind of standing electromagnetic wave on any normal cutting plane of the small spherical surface is “c” in logic.
We notice that this not yet enough to represent the mass – energy relationship because the circle is just a line on the spherical surface while the whole model is a small spherical surface.
Because the simplest relationship between “surface” and “line” is “square” in logic, the simplest relationship of energy - mass should be “c²” in logic.
(Note: Actually the elementary particle model in X4 Theory should be a spherical surface. But for intuition sake, the “circle kind standing wave” can serve as a simplified model. And for convenience in calculation in chapters below, the simplified model is applied. And it’s considered that the energy on the spherical surface be converted entirely into the “circle kind standing wave”.)

When the spherical electromagnetic wave demonstrates only the property of mass, it doesn’t mean that it has no energy;
The same principle, when the released photon demonstrates the property of energy, it doesn’t mean that it has no mass.
It’s just that thing. So, for a photon, E = E0, m = m0.

Next, we use a mathematical method to analyze what’s the mass of a released photon:
In stationary situation (spherical electromagnetic wave), E0 = m0 c²;
In dynamic situation (travels in straight line), E = m c².
Because E = E0, then, m c² = m0 c², namely m = m0.

Since the inversion of the chirality of the spiral spring does not result in the inversion of its mass, the inversion of the chirality of the circle kind of standing electromagnetic wave should not result in the inversion of its mass either. So, X4 Theory considers that the anti particle also has the positive mass.
Also the inversion of the chirality of the circle kind of standing electromagnetic wave does not result in the inversion of the relationship of energy - mass c².
So, X4 Theory considers that the anti particle also has the positive energy.

Liqiang Chen
Nov 7, 2020
给他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁一个超文革赛阎王光荣称号快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

In this post, piggy explores how to use the X4 physical model for elementary particle to solve a problem in physics:

“Using the principles of relativity one can derive the expression for the kinetic energy of, K, of a particle. As v -> c, K -> infinity.” (Note: this is a post of an American physicist in another site. He was directing some research.)

So, sounds that a photon’s kinetic energy should be infinite?
…………………………………………………
According to the physical model of elementary particle ahead (for intuition sake, the simplified model better), an electron could be considered as a small round ball (the simplified model a circle) with the size / radium of r.
When the electron is moving, according to the length contraction principle of SR, r decreases. According to the mass – space equation m ∝ 1 / r, the mass of the electron increases. According to the equation Ek = mc² - m0c², the kinetic energy of the electron increases. When v → c, r → 0, the mass of the electron m → ∞, the kinetic energy of the electron Ek → ∞. Of course, r never can reach 0 because that means the electron disappears, non sense in physics. That’s why v can’t reach c.
According to the physical model of released photon ahead, the released photon is not the same MATTER STATE as the electron. There is no a specific shape / size / radium for the released photon. So, logically speaking, the rule of v → c, r → 0, m → ∞, Ek → ∞ is not applicable to the released photon.

Liqiang Chen
Nov 11, 2020
给他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁一个超文革赛阎王光荣称号快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Below is research in respect of “spherical electromagnetic wave” revealed by a scientist from Ukraine.
https://physicshelpforum.com/threads/cold-synthesis-ball-lightning-a-brewing-scientific-revolution-online.16080/
他江门地方黑恶势力钟永康集团及新会一中九一四班姓蔡的万岁，万岁，万万岁！当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Now the problem associated with the speed of photon (for details in this respect, please see the thread “How to understand the energy – momentum equation in a natural way” in the Relativity forum) can have a thorough / explicit solution here.
The X4 physical model demonstrates that a released photon is “a section of electromagnetic wave”. So, of course, it naturally propagates away (travels) in the light speed c. Such additional condition as “massless” to “force” it to realize is just conjecture in math game due to unknown of what’s a released photon in physics.
A vivid analogy:
The water wave naturally propagates away in its constant wave speed in the pool.
While the football can sit, when you kick it, it moves. If you kick it more powerfully, it moves faster.
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Neutrino vs photon, touchy and feely:
Neutrino and photon are both neutral particle (non - charged);
Piggy heard some theoretic physicists (such as Toppy sir) said that neutrino moves at light speed in vacuum; also piggy heard some experimental physicists said that neutrino moves at nearly the light speed in vacuum. No matter what it is, that means their speeds are no much different.
The question / emphasis here is that why the penetration ability of neutrino is extremely strong while the penetration ability of photon is so weak?
There might be many methods to argue one phenomenon. Also there might be one method to explain as many phenomena as possible.
………………………………….
The approximate relationship between the collision chance and the speed / size could be seen in the file of Department of Physics and Astronomy, University of Leicester.
https://physicshelpforum.com/threads/raining-an-ordinary-topic.15321/post-44305

In the X4 physical model, the shape of neutrino is also a small round ball (simplified model a circle). That means it can just move at nearly the light speed in vacuum. Its size might contract to very tiny. Then, that means the collision chance with other particles is very small when the neutrino shot into the medium (such as the Earth).
But the released photon is not the same situation. The X4 physical model demonstrates that a released photon is “a section of electromagnetic wave”. It has much more chance to “say hello” to others particles in the medium.

Liqiang Chen
Nov 22, 2020
他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Okay, guys who are willing to touch the elephant in an alternative way go ahead with piggy. And after piggy dead, go ahead yourself. haha

The continued topic of the mass – space equation:
The derivation of the mass – space equation L ∝ 1/M from macroscopic angle could be seen in the thread “cosmos vs us”. Hereby, we derive it from microscopic angle.

First, there is a question, why the energy equation for a released photon is E = hγ in Quantum theory and need not to take the number of crests (n of λ, here n is a natural number) into account?
In X4 physical model, a released photon is just a section of electromagnetic wave, its energy E should ∝the number of crests (n of λ).
It implies that all released photons have the same number of crests (n of λ)? Temporarily suppose it is and see what will happen.
Next, we refer to the simplified physical model (circle kind standing wave). Unfold the standing wave, it turns into two released photons (for simplicity sake, just consider that it’s one released photon).

We watch the game in counter way, it’s one released photon turn into a standing wave.
And we got: standing wave which constitute all kinds of elementary particles have the same number of crests (note: nt of λt, when referring to travelling waves; and ns of λs, when referring to standing waves. The lower index “t” means travelling wave while “s” means standing wave in this context).


Next, we try to use the X4 physical model for elementary particle and the temporary conclusion of same number of crests in this chapter to calculate the radius of elementary particle.
Below, we calculate the central line of the helical track of layer instead of the helical track itself because the speed of light should be calculated on the central line. And the wavelengthλt should be the projective wavelength on the central line.
E = Mc² = 2hγt = 2hc / λt then:
λt = 2h / Mc then:
The radius of elementary particle is:
r = ntλt / 2π = nth /πcM
Because nt, h, π, c are all constants, we use a constant “a” for simplicity and a = nth/πc, then:
r = a/M
Namely, r ∝1/M. In fact, it’s the same meaning as L ∝ 1/ M ahead.
The existence of the mass – space equation does not depend on reference frame / movement / SR.

Liqiang Chen
陈力强
Nov 24, 2020
给他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁一个超文革赛阎王光荣称号快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

Piggy doesn’t know whether Lorentz could provide any experiment to verify that the space does not contract in the cross direction of movement. But I can provide an experiment to verify the mass – space equation directly. It’s the μ Hydrogen phenomenon.

When the electron of a Hydrogen atom is replaced with a μ particle, the atom turns to be μ Hydrogen. For detailed information, see relevant publications.
There is a phenomenon occurs: the radius of the proton in μ Hydrogen atom contracted. Why?
Below we try to use the conclusion in the mass – space equation to explain it.

The radius of the proton in Hydrogen atom is r1 ≈ 8.768×10ˆ-16m. The mass of an electron is Me ≈ 9.1×10ˆ-31kg, while the mass of a μ particle is Mμ ≈ 200 ×9.1×10ˆ-31kg.
The mass of a proton is Mp ≈ 1.6726×10ˆ-27kg.

The reduced mass of the electron in Hydrogen atom is:
μ1 = Me Mp / ( Me+ Mp) ≈ (9.1×10ˆ-31) ×(1.6726×10ˆ-27)/ [（9.1×10ˆ-31）+(1.6726×10ˆ-27)] ≈ 9.0951×10ˆ-31kg

The increased mass of the proton in Hydrogen atom is:
M1 = Mp+ Me -μ1 ≈ (1.6726×10ˆ-27) + (9.1×10ˆ-31) - (9.0951×10ˆ-31) ≈1.6726×10ˆ-27kg

The reduced mass of the μ particle in μ Hydrogen atom is:
μ2 = Mμ Mp / ( Mμ+ Mp) ≈ (200×9.1×10ˆ-31) × (1.6726×10ˆ-27) / [（200×9.1×10ˆ-31）+(1.6726×10ˆ-27)] ≈ 0.1641×10ˆ-27kg

The increased mass of the proton in μ Hydrogen atom rise to be:
M2 = Mp+ Mμ –μ2 ≈ (1.6726×10ˆ-27) + (0.182×10ˆ-27) - (0.1641×10ˆ-27) ≈1.6905×10ˆ-27kg
According to the mass – space equation r ∝1 / M, the rise of the increased mass of the proton leads to the contraction of the radius of the proton in μ Hydrogen atom.

Liqiang Chen
陈力强
Nov 25, 2020
给他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁一个超文革赛阎王光荣称号快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

This post is a bit odd.
First, piggy invites guys to take a look at the what coffin box from what CN said in piggy’s thread in PHF.
https://physicshelpforum.com/threads/the-game-of-match-sticks.16181/post-50090

But if you are a guy who believes in the philosophy of touching the elephant, then please go ahead with piggy.
………………………………………………..
SR vs X4 physical model of elementary particle vs QM, touchy and feely:

We also notice that the standing wave condition is not the sufficient condition but the necessary condition. Namely, when Cir = 2πR = m(λt /2) is satisfied (here m is an integer, not mass), there is still a probable situation that no stable standing wave formed. This cosmos has two aspects: one certain aspect as well as one uncertain aspect. This is the “certain – uncertain duality”.
The habitual name of “particle” is just the certain aspect of the “certain – uncertain duality”, namely the standing wave formed. In this aspect, concrete shape is formed and trajectory could be employed to describe movement.
In the uncertain aspect, no concrete shape is formed and trajectory could not be employed to describe that situation. It might be all kinds of states. The appropriate method of description is “superposition of states”.

In respect of the traditional conception of “wave – particle duality” (wavicle), piggy has illustrated ahead in the stuff about the X4 Unit Charge Model that “wave” is wave characteristic of electric interaction. “Particle” is also the certain aspect of the “certain – uncertain duality”.

Why I can derive the mass – space equation in two different methods, both Einstein’s SR and my own physical model? What natural secret is hidden behind this? It demonstrates that the dynamic and the static are equivalent in a background sense.

The X4 physical model demonstrates that the basic principle of SR and QM are both reasonale.

Liqiang Chen
陈力强
Dec 1, 2020
给他江门地方黑恶势力钟永康集团及新会一中九一四班谁谁一个超文革赛阎王光荣称号快快全世界全宇宙打靶啦。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

You confuse Ontology with Epistemology...common mistake. The uncertainty principle is grossly miss portrait as referring to a wave function being in a quantum superposition of states before it is measured. It is false. We attribute probabilities to a particle in attempts at prediction and control because we CAN'T KNOW its actual location or momentum, an epistemic problem that is. The wave function HAS a definite STATE, an Ontological factual status. We just happen to NOT KNOW it until we measured it, and even then we can know only one of the two, either momentum or location.

You are really not a simple guy. And a2k seems not a simple place.
“This cosmos has two aspects: one certain aspect as well as one uncertain aspect. This is the “certain – uncertain duality””. What piggy means is the “superposition of states” principle rather than the what Heisenberg’s uncertainty principle.
The what Heisenberg’s “uncertainty principle” is far beyond the present topic.
Have a lovely weekend first, guys.