Macro vs Micro

If you take a big enough sample size, variations will average out and you can make statements that you can't on small samples. A bowling ball traveling through air can be modeled much more simply than an alpha particle or a neutron.

You seem to be one of those people who still try to find out the border between the macroscopic and the microscopic…

How big the size of the bowling ball can realize “variations will average out”? The size of “an alpha particle or a neutron”? You not yet found out the border. And what does “variations” mean in physics?
…………………………………………………………..
Assume the border is the size of “an alpha particle” L in rest frame S. But view from the moving frame S’, the size of “an alpha particle” will be L’ < L. Physics rule will be not equally applicable in different inertial frames..
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打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

you ought to get involved in a discussion about macro v micro among chemists or geneticists.

Its a word that has so damn many associations that its almost useless

“you ought to get involved in a discussion about macro v micro among chemists or geneticists.”

This tramp in cosmos heard an authentic physicist (Toppy sir) said elsewhere that “to find out the border between the macroscopic and the microscopic is a big deal in physics.” It concerns the issue of when QM is applicable in their eye. Seems that you not so agree with those guys. But physics should be one thing, not alike gene…

“Its a word that has so damn many associations that its almost useless”

Actually, this tramp in cosmos agrees with your opinion, more or less.
The fact is that people not yet found out the border between macro and micro up to this day while they use both the classical physics and QM. A good solution might be that the classical physics describes the certain aspect of cosmos while QM describes the uncertain aspect of cosmos.
At this moment, the more meaningful idea might be the word “wavicle”.

Below is a story in a report many years ago:
A professor asked a student: why a (moving) glass seems to have no wavicle character?
The student answered: because the Duck de Brogiel wavelength is too short, people is not easy to perceive it. (λ = h / p, for a glass, p is big enough to render λ very small)
The professor kept silent.
Why? Maybe he was thinking: why we can't see the train jumping on the trails before it stops? (p trends 0, λ trends to ∞ )

Someone might say that “What is the amplitude of the wavicle?”
But another one might answer “Who knows? It's not mechanic wave...”.

Someone might have an idea “I am guessing that the positional probability function for a train will drop to truly miniscule levels, beyond practically measurable distances of its Newtonian position.
When does truly miniscule probability become impossibility?”
But another one might answer “The test question is the glass. If I’m that student, below is my answer.
ATHENTIC QM: the glass is a neutral big free particle, so︱A︱² is a constant. It has nothing to do with λ, even xyz or t. It means that the probability of presentation of the glass at any space point is the same. That’s to say I can see the glass everywhere. Sir, a large glass of beer please? And then you will see it too…”

A special dimension is needed to accommodate the uncertain characteristic so that QM can fit with fact and become an excellent modern theory. That’s the state dimension X4. (the primary conception of X4 Theory can be found in the thread “can projective geometry find out its application in physics?” in the geometry column. Piggy just move one sentence here: we use capitalized letter to represent physical quantity in 4D space.)
……………………………………………

Wave Functions in 4D Space (Ⅰ)

Once upon a time, in the equation X = X4x and then the equation V = X4v, the reference in fact is 3D space.
In order to prevent losing the meaning of contrary or reference, in 4D space wave function, we engage that space and momentum, one is 4D space physical quantity, then the other is 3D space physical quantity. This is called the 1/2 Rule or the Special Engagement.
1. The position space wave function for a free particle in 4D space is:
Ψ(X, t) = A exp ( i(p •X – Et )) Amplitude A is a constant. (omit “ℏ” and vector marks for convenience of observation)
X = X4x
Then, the probability density｜A｜² is a constant. It means the probability of appearance of the particle in any point of 4D position space is the same. In turn, it means the probability of the X4 state the free particle be in is the same. The situation is the same in any position x in the 3D space.
Because it’s a free particle, no interaction is concerned, the above analysis reflects the property of the particle itself regardless it is moving with any momentum p in the 3D space or not (It has nothing to do with wavelength λ = h / p ).
2. The momentum space wave function for a free particle in 4D space is:
Ψ(P, t) = A exp ( i(P•x – Et )) Amplitude A is a constant. (omit “ℏ” and vector marks for convenience of observation)
P = X4 p
Then, the probability density｜A｜² is a constant. It means the probability of appearance of the particle in any point of 4D momentum space is the same. In turn, it means the probability of the X4 state the free particle be in is the same. The situation is the same in any position x in the 3D space. Because it’s a free particle, no interaction is concerned, the above analysis reflects the property of the particle itself regardless it is moving with any momentum p in the 3D space or not (It has nothing to do with wavelength λ = h / p ).

Look at the 3D space wave function for free particle in QM again.
Ψ = A exp( i(p•x– Et )) omit “ℏ” and vector marks for convenience of observation.
When position x and momentum p are both determined at the same time, it will no longer be a wave function, instead, an oscillation function. It seems that the “wave character” should disappear either.
What interesting is it could be considered as a special situation and the calculation of probability is still applicable. “A” is a constant. ｜A｜² is a constant. It means the probability of appearance of the particle in any space point is the same. In turn, it means the position of the free particle can not be determined.
Contradiction…
Next, resort to 4D space wave function. In the item p •X or P•x, among space and momentum, if one physical quantity is 3D space quantity, then the other is 4D space quantity. It reflects that they two can not be determined simultaneously and avoid the dispute.
Classical physics describes the certainty in 3D space while QM describes the uncertainty in 4D space.
…………………………………………………
In QM, there is the appearance of position space as well as the appearance of momentum space. The physical reason behind them is just the state dimension X4.

Liqiang Chen 陈力强
Sept 8, 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打靶就二十一世纪绝对全世界第一。当今时代，全世界没有什么人能够值得如此殊荣。呵呵

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.
……………………………………………….
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 can’t.
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.
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

X4 Model of Unit Electrical Charge vs the Wave Characteristic of Electric Interaction

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 be Ψ(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 of electric charge and has no contradiction to facts:
1. Under such a model, electric field or say unit electric (charge) interaction between basic particles will be just the determination of probability method of existence each other. According to the wave function Ψ(P ) =（1/r）sinr P , it only has something to do with distance (∝1/r or say∝|1/r|² = 1/r²).
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.

Moreover, 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
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

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
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

Unified Information of Inference in the Double Slits Experiment of Electron

In the traditional idea, the “superposition principle” was employed to explain the interference pattern:
The calculation is about as below:
“Ψ = Ψ1 + Ψ2 is also a possible state of the electron.
Then, the probability of electron could be found in space is:
｜Ψ｜² =︱Ψ1 + Ψ2︱² = … = ︱Ψ1︱² + ︱Ψ2︱² + (interference item)
And just because of the existence of the interference item, the interference pattern appeared.”
But the X4 unit charge model ahead demonstrates that the wave function of free particle is just a mathematical form while the wave meaning in physics actually already lost.
In X4 Theory, the “superposition principle” is just as simple as 2.6 = 1.1 + 1.5, etc. No information of interference could be generated.
So, the employment of the “superposition principle” to explain the interference pattern in the traditional idea is just operation in math while has no substantial physical meaning of interference.

……………………………………………………………….
Next, piggy introduces how the X4 unit charge model provides an explicit mechanism to provide and guarantee the unified interference information in the slits.
For convenience and intuition sake, assume a most simplified apparatus: only one electron on the gun and only one electron is moving in the apparatus.
No matter which slit the electron passes through, the wave characteristic of electric interaction will cause interference information in the slits. Because the positions of the slits are fixed, the wave functions of electric interaction for all of those electrons are the same. Approximate expression is: Ψ(P ) =（1/r）sinr P. (r is the distance between the gun and the slits)
Here “P” is 4D space momentum. P = X4*p, p is 3D space momentum and p = mv. The precision of the apparatus guaranteed the velocity of every electron is the same when it reaches the slits. Then, the momentum p is the same. λ = h / p is the same. (Note: wavelength should be a conception in 3D space.)

(to be continued)
(Piggy will supplement the relevant picture as soon as I got another site to host the pictures)
Liqiang Chen
陈力强
Dec ,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

(continued)

The physical mechanism of the generation of probability by the wave characteristic of electric interaction:
No matter in the single slit or double slits experiment of electron, on the diffraction pattern or the interference pattern, the areas of bright strips means electric interaction exists while the areas of dark strips means electric interaction does not exist.
At this time, the electron presents its certain property in 3D physical space. According to the X4 physical model of elementary particle, it’s a tiny round ball.
The tiny round ball has to drop onto one of the areas of bright strips on the screen / film RANDOMLY. This is the first step of the generation of probability.
And then, the tiny round ball has to drop into one point of the area of bright strip chosen in the first step above RANDOMLY. This is the second step of the generation of probability.
(Piggy will supplement the relevant picture as soon as I got another site to host the pictures)
Liqiang Chen
陈力强
Dec ,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

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

Supplement of the diagram of the spiral spring:

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 suggest those guys who insist the point that there is a border between the macro and the micro stop talking physics until they have found out that border. Otherwise, how can they assure whether it’s appropriate to use QM to describe the behavior of an electron or use the classical mechanics to describe a large rabbit bouncing?

Since the conception of matter wave / probability wave can not be compatible with Relativity nor classic mechanics nor classic electromagnetism. And as piggy said ahead that actually the electron is moving in electric field in the apparatus, there is another possibility that the diffraction and interference might be caused by the wave characteristic of electric interaction. And my own theory can be compatible with Relativity as well as classic mechanics and classic electromagnetism.
The great philosophy told us that “all sciences are interconnected”.
So, hereinafter, piggy decides to touch the elephant in my own way. Piggy retains the conception of wave function because it’s reasonable in my model. But piggy considers that its true physical meaning should be found out. Also, piggy thinks that the calculation method as well as the operators in traditional QM remains applicable.

Due to the persistent disturbance in the thread “the base of physics” from one stubborn guy, and the pictures here seems gone again. Piggy has to come back to this thread in advance and do something:
Piggy hereby officially gives up the traditional conception of “probability wave” and so the sentence “Under such a model, electric field or say unit electric (charge) interaction between basic particles will be just the determination of probability method of existence each other” in the unit charge model ahead hereby eliminated.

Now, piggy has a try to supplement the diagrams for the second time.
Double slits experiment of electron:

The physical mechanism of generation of probability:

The spiral spring: