MTL - Into Unscientific-Chapter 454 very different results (on)
Chapter 454 Completely different results (Part 1)
Arithmetic table.
Looking at the two general solutions with exactly the same content in front of you.
While rejoicing at the breakthrough of a difficult problem, Xu Yun also felt a little emotion in his heart again.
He thought about what happened in Jinping's deep underground laboratory more than a week ago.
At that time, the re-inspection team composed of many academicians also encountered a very serious problem, and got stuck in the accuracy of the energy level of the W-boson.
The result was that everyone was thinking hard and had no results.
Wang Lao, who is over a hundred years old, stepped forward.
He proposed a plan to use J particle optimization, and successfully solved this problem, which led to a series of things later.
Today.
How similar is Yang Lao's appearance this time to Wang Lao?
The same age is over a hundred years old, the same is not in good condition, and the same blow goes straight to the key point
"A family with an old man is like having a treasure"
Xu Yun sighed deeply, turned his head and looked at Zhou Shaoping opposite him.
Both of them saw an idea in each other's eyes:
Must not waste all of Yang's hard work!
Say something that may not sound very nice but is true.
For an elder of Mr. Yang's age, this kind of plan that accurately covers specific procedures consumes his lifespan!
Think here.
Xu Yun picked up the pen again, and quickly proceeded to the next calculation.
Now with this point raised by Mr. Yang, the first step taken by Xu Yun and Zhou Shaoping is only a matter of calculation.
After all, Mr. Yang gave a general solution.
Tongjie refers to the literal meaning of the word Tongjie, and it is not difficult to understand its use.
So soon.
Xu Yun obtained a brand new 'state' based on the energy operator E^=itφ and the free field as the eigenfunction of energy.
This ‘state’ refers to the ground state of the system before the vacuum state when the ‘Pluto’ particle does exist.
This involves particle physics. Or a very important model in quantum mechanics.
That is, energy is quantized, and there is an operator in this model called nk.
It means that the model has nk particles of wavenumber k—yes, nk k, not n k.
According to the general solution drawn by Xu Yun and the others, it is not difficult to see.
When nk=0.
There is no particle in the system, but its energy is not 0, and its wave function is not 0 either.
This is a vacuum system, so the energy of "vacuum" is not zero.
That's right.
This is the prototype of the famous vacuum zero-point energy theory. However, concepts such as virtual particles need to be supplemented, which has nothing to do with the current situation, so I will not mention it for the time being.
all in all.
The state obtained by Xu Yun is the state before a system with 'Pluto' particles is transformed into a vacuum.
The general solution operator of this state is called the possession operator, which has a normalization factor.
This normalization factor is a core data that Xu Yun and Zhou Shaoping are looking for this time.
Using a less rigorous but easy to understand example to describe is
We want to describe and locate a point on the plane. The simplest and most appropriate way is to express its position with the XY axis.
That is (4, 2) or (8, 3) and so on.
The normalization factor is equivalent to the X-axis coordinate.
The normalization factor is locked, and the rest of the link is naturally to find the Y-axis coordinates.
Once the two "coordinates" are all found, then the final goal can be locked.
Of course.
The actual normalization factor is a description of a probability distribution, which involves combinatorics, so I won’t go into details here.
"X-axis coordinates"
In the live media area, Chen Shanshan repeated the word, and asked Zhang Han curiously:
"Dr. Zhang, if the possession number operator is regarded as the X-axis coordinate, then what is the Y-axis coordinate that is needed?"
Zhang Han thought about it and explained:
"The state calculated by Dr. Xu and Academician Zhou is located in a specific configuration space. The relevant content can be found in Chapter 8, 8.2 of Mr. Zeng Jinyan's "Tutorial of Quantum Mechanics", the second edition, specifically on page 151."
"So in addition to the possession operator, they had to compute a modulus square operator with an even number of permutations."
Chen Shanshan blinked:
"Modulus square operator?"
Zhang Han nodded affirmatively:
"Yes."
at the same time.
Lu Chaoyang, who had been watching Xu Yun's progress from the audience, also wrote down the words "modulus square operator" on the paper and drew a circle.
That's right.
After calculating the possession operator.
The next step for Xu Yun and Zhou Shaoping is to calculate the modulus square operator of the ‘Pluto’ particle.
Or to be more precise.
Angular Momentum.
Students who were particles in their previous life should know.
Talking about the properties of a certain particle is actually talking about the characteristics of the Lagrangian of the field of this particle.
In this way.
The particle properties can be divided into two types:
The characteristics that can be reflected by the Lagrange quantity, and the particle characteristics that are reflected by the interaction.
Among them, there are many particle properties that can only be reflected through interactions, for example, the most representative concept is the concept of charge.
The so-called charge is actually the Noether charge derived from the U(1) symmetry of the complex field.
When considering the localization of U(1) symmetry, it is necessary to introduce some massless vector field to interact with this complex field.
If this massless vector field is an electromagnetic field, then the above-mentioned Noether charge is interpreted as an electric charge.
As for the free particle Lagrangian, the particle properties that can be directly reflected are relatively few, and there are only two kinds in total.
One is the mass of the particle, which is given by the coefficient of the Φ term in the Lagrange scale.
The second is the spin of the particle, which can be given by the Noether flow of the Lagrange quantity under the space rotation transformation.
For the 'Pluto' particle.
Currently, including Xu Yun and Wei Teng, no one can calculate the mass of its particles—because of insufficient information.
But spin is different.
There is a bad saying in particle physics, that is, spin is an intrinsic property of particles.
What does intrinsic mean?
When the police interrogate a person in a TV series, everyone should have heard this sentence more or less:
"xxx, your disposition is actually not bad, it's just that you lack the correct guidance. After you go in, you should reform yourself and try to become a good person."
The disposition in this sentence is actually the same as the intrinsic nature of particles to some extent. It belongs to the "innate" attribute, and it will not be transferred by the environment at the beginning of its birth.
For example, a pigeon who writes a novel. Although he owes dozens or hundreds of chapters to update, his own temperament is actually not bad, but he is a little lazy.
Of course.
This is just a metaphor.
In fact, the intrinsic properties of particles are very complicated, involving gauge symmetry.
For example, the chubby Nima next to Xu Yun—here I will explain again, her name is really Nima, and her English name is NimaArkani-Hamed.
A few years ago, Nima once said a famous sentence:
3 is not equal to 2, which is gauge symmetry, and 2 is not greater than 3, which is intrinsic.
all in all.
Just like a two-dimensional surface such as a sphere does not depend on being embedded in a three-dimensional space, so curvature is its intrinsic property, and the modulus square operator is also an intrinsic property that can be calculated mathematically.
As long as the modulus square operator is determined, plus the previous occupancy number operator, the probability position of the ‘Pluto’ particle can be locked.
Or to be precise.
This is a mathematically probable position, and whether it can be captured or not requires actual operation.
If the Jade Emperor is not prepared to give face to the God of the West in his own territory, Wei Teng may end up with a bamboo basket to fetch water in vain.
"Xiao Xu."
After confirming that he was ready to calculate the modulus square operator, Zhou Shaoping pondered for a moment, and said to Xu Yun:
"In this way, the derivative of the spherical coordinate base vector with respect to each coordinate variable is left to you, no problem?"
Xu Yun flipped through the file and nodded quickly:
"no problem."
After he finished speaking, he paused, hesitated for a moment, and added another sentence:
"Academician Zhou, why don't you leave the radial and angular decomposition to me?"
Xu Yun's remarks were not to show off his strength, nor to grab the show, but to worry about Zhou Shaoping's body.
Although Zhou Shaoping is a round younger than Yang Lao, he is also approaching 90 years old. He has been busy for so long today, and the physical and energy consumption is actually very large.
He, a 25-year-old young man, was a little tired at this time. Zhou Shaoping's situation must be worse, but he just kept holding on.
Actually it’s not just Zhou Shaoping.
Except for the 50-year-old "young man" Nima, the rest of Higgs, Tehooft, and Polyakov are all 80-90 years old, and their energy consumption is not low at this time .
It’s just that the current situation is called group calculation, but it can also be regarded as a silent battlefield in essence. They were all from the Netherlands, and Polyakov's assistant was a bear.
Thus, although everyone was tired, no one was willing to leave first.
Zhou Shaoping obviously understood this too. After he thought for a while, he quickly nodded:
"Okay, thank you for your hard work, Xiao Xu."
Hear this statement.
Old Yang who was opposite Zhou Shaoping couldn't help raising his head and gave him a light glance.
Although Mr. Yang spent the first half of his life abroad all year round, he returned to China at the end of 2003. He did not have much entanglement or contact with domestic scientific research factions.
But Zhou Shaoping is also well-known internationally, so Mr. Yang has heard of his character and experience.
In the early years, Zhou Shaoping had a student he liked very much, who was extremely talented. In his sophomore year, he was accepted as a disciple by Zhou Shaoping, who had already been elected as an academician.
A few years later, that student was admitted to graduate school and successfully entered Zhou Shaoping's project team.
The result is in an experiment.
Because Zhou Shaoping had been working overtime and was in poor health, the student offered to share part of the project for Zhou Shaoping, and Zhou Shaoping naturally agreed.
result
The student made a calculation error in a certain link, which caused the light source to overflow due to the excessive magnitude, causing serious damage to the equipment.
In the end, the whole project fell short, and the funding of more than 5,000 yuan was in vain.
To know.
That was five thousand dollars in 1983.
At the same time, because the experiment used a first-generation radiation source, the radiation rays beyond the limit directly passed through the longitudinal gradient dipole magnets, causing the four recent researchers to be irradiated and suffered severe thermal radiation burns.
One of them died three years later, one had extremely serious sequelae in his lungs, and one was blind in both eyes.
That's right.
This was the accident that happened at the Huairou base, and it was also a very disastrous experimental accident in the history of high energy physics in China.
The staff member who was blind was Zhou Shaoping's student Huang Wuxiang.
Since then.
Although Zhou Shaoping is cheerful and doesn’t lose his temper on weekdays, he has a very strange persistence in research:
He will never entrust others to do any assigned tasks.
Zhou Shaoping has maintained this habit for 40 years, but he did not expect that today he would
Make an exception?
Is it because of lack of energy?
Old Yang glanced at Zhou Shaoping, then shook his head slightly in his heart.
Not quite.
Although Zhou Shaoping did look a little tired, neither his complexion nor his computing efficiency were far from the level of "can't hold on".
And since it is not due to physical strength, then there is only one answer—
Zhou Shaoping met a junior he could truly trust, and his confidence was so strong that it forcibly overwhelmed the nightmare in his heart.
Think here.
Old Yang quietly glanced at Xu Yun beside him again, with a subtle expression on his face.
Zhou Shaoping, Zhang Gongding, Hou Xingyuan, Wang Lao. Oh, and Yang Lao himself.
Unconsciously.
This young man has had contact with so many academicians of the older generation, and has received their recognition and help, and has been given high hopes by one old academician after another.
Looking at the young generation in the Chinese scientific community, Xu Yun is the only one.
But it is very interesting.
He himself doesn't seem to realize this?
Actually, if Xu Yun can catch up to this chapter, he may be able to understand what Elder Yang is thinking through the content of the text.
But unfortunately, he does not have this ability.
So at this time, he didn't think about expectations or trust at all, but devoted himself to the calculation of data.
After all, this is the final boss.
With the blessing of Dirichlet, Xu Yun's mind became clear.
Swish Swish Swish—
A large number of formulas appeared one after another on the calculation paper with the movement of the pen tip.
The modulus square operator contains both the position operator and the momentum operator, and there is a very precise commutation relationship between them.
If it is a particle measured through a phenomenon, it is actually very easy to deduce it, just set a template.
But the problem is that the 'Pluto' particle has not been captured, so the derivation process is very troublesome.
And Xu Yun’s entry point for this preparation is
Poincaré group.
Because the Poincaré group has a very special place:
Its representation can be completely determined by its obsessive subgroups and induced representations.
With the help of the representation of the small group of the universal cover of the Poincare group on the spin space, the irreducible unitary representation of the universal cover on the Hilbert space can be obtained, that is, the induced representation.
Different directional subgroups give different induced representations, corresponding to different single particle states.
That is, the irreducible unitary representation of particles is completely determined by the basic symmetry of space-time, and there will be no interference from other factors.
Well, the above passage is standard Chinese characters and human words.
After a while.
Xu Yun wrote down the eigenstate of the operator l^z with the eigenvalue of m under the calculation content of the secret level:
l^+ψm=Cψm+1
At the same time [l^z, l^+]=l^+ can get l^zl^+=l^++l^+l^z=l^+(1+l^z), so it can be seen that l^+ is quite For a generation operator, l^ is equivalent to an annihilation operator.
They make the eigenvalues of l^z always increase or decrease by an integer 1 in turn. When the square of the modulus of angular momentum is fixed and the maximum eigenvalue of l^z is m=l-1, then there must be l^+ ψl=0.
See here.
Maybe some Zhou Zhou students feel a little strange:
Why is the largest eigenvalue m=l-1, shouldn’t it be equal to l?
the reason is simple.
Because when the square of the modulus of angular momentum is fixed and l is the maximum allowable value of m, the state with eigenvalue l+1 does not exist.
Because the system can always be in the state where the orbital angular momentum is 0, so 0 must be an eigenvalue of the component operator l^z.
From the behavior of l^+ and l^, we can see that for the angular momentum component operator l^z, the difference between its adjacent eigenvalues is always an integer 1.
So the eigenvalues of the component operator l^z can only be m=0, ±1, ±2, .±l-1.
Of course.
Xu Yun was able to think of this, largely due to the vision he had at this time.
Just like Witten and the others ignored the distortion of the lone base vector before, the state of l+1 is not in the normal verification range, and there are many more important processes than it.
And once the calculation is wrong here
Then this derivation, at least the derivation of the Academy of Sciences team represented by Zhou Shaoping and Xu Yun, will completely fail.
solves this problem, and all that's left is binary spinors.
During this process.
The eigenvalue σ of s^z needs to be regarded as a variable, then the spin wave function of the particle is a function of σ—as mentioned earlier, the spin of Pluto particles is a semi-odd number, that is, 1/2, 3/ 2 or 5/2 etc.
Therefore, its matrix factor has only one form:
ξ′1η′2ξ′2η′1=(αδβγ)(ξ1η2ξ2η1).
This is a combination of two binary spinors, a scalar in the space of binary spinors.
Write here.
Xu Yun flipped through the previous data again.
"Sure enough. The determinant is equal to 1, which is the real reason why the value of flux is too large."
Actually, in the previous process, Xu Yun always felt that there was a doubt that had not been answered:
That is, in the calculation of isolated point particles, the expected background is 3.2fb^-1—this is the data he personally detected, and he has detected it more than once.
But the corresponding flux value still becomes larger. Although the phenomenon seems to be due to the influence of the ‘Pluto’ particles, there is no suitable explanation for the spatial operator.
Now it seems
The reason is because the transformed determinant is equal to 1.
That is, its external constraints have changed.
Because for non-relativistic cases, the physical meaning of ξ1ξ1+ξ2ξ2 is the probability of finding a particle at a certain point in space.
Therefore ξ1ξ1+ξ2ξ2 must be a scalar, that is, there should be:
ξ′1ξ′1+ξ′2ξ′2=(Uκ1ξκ)(Uκ1ξκ)+(Uκ2ξκ)(Uκ2ξκ)=ξ1ξ1+ξ2ξ2.
But for the case of relativity theory, the physical meaning of ξ1ξ1+ξ2ξ2 is no longer the probability of finding a particle at a certain point in space, but the time component of a four-dimensional vector.
That is, it has only 3 independent real parameters, and one of them is fixed. Wait!
Suddenly.
Xu Yun paused abruptly as he moved his pen on the paper, and a somewhat horrifying thought popped into his mind.
"Fuck, it can't be that thing, right?"
Note:
Grandpa and grandma are about to be discharged from the hospital, and there should be a small explosion next month, yes.
(end of this chapter)
