Chapter 452: Completely different results (Part 1)
On the arithmetic table.
Look at the two general explanations in front of you that have exactly the same content.
While rejoicing at the breakthrough of a difficult problem, Xu Yun also felt a trace of emotion in his heart again.
He thought of what happened in Jinping Dishen Laboratory more than a week ago.
At that time, the reexamination team composed of many academicians also encountered a very fatal problem, which was stuck in the energy level accuracy of W-boson.
As a result, everyone was thinking hard to no avail.
Mr. Wang, who was over a hundred years old, stood up.
He proposed a J-particle optimization plan and successfully solved this problem, which led to a series of subsequent events.
Today.
How similar is Mr. Yang's appearance to Mr. Wang?
Both are over a hundred years old, in the same poor condition, and with the same direct hit to the key point...
"Having an elder in the family 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:
Mr. Yang’s hard work must not be wasted!
Let me say something that may not sound nice but is very true.
For an elder of Mr. Yang's age, this kind of plan that accurately covers the specific process will consume his life!
Think of this.
Xu Yun picked up the pen again and quickly made the next calculation.
Now with Mr. Yang's suggestion, the first step taken by Xu Yun and Zhou Shaoping is only a matter of calculation.
After all, what Mr. Yang gave was a general explanation.
By looking at the literal meaning of Erziguan, it is not difficult to understand its purpose.
So very quickly.
Xu Yun obtained a brand new ‘state’ based on the energy operator E^=?i??tφ and the free field being the eigenfunction of energy.
This ‘state’ refers to the base state of the system before the vacuum state when ‘Pluto’ particles do exist.
This involves particle physics...or a very important model in quantum mechanics.
That is to say, energy is quantized, and there is an operator in this model called nk.
It means that the model has nk particles with wave number k - yes, nk k particles, not n k particles.
It is not difficult to see the general explanation obtained by Xu Yun and others.
When nk=0.
There is not a single 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 0.
That's right.
This is the prototype of the famous vacuum zero-point energy theory. However, concepts such as virtual particles need to be added, which have 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 of a system with Pluto particles before it is converted into a vacuum.
The general solution operator for this state is called the possessive number operator and has a normalization factor.
This normalization factor is the core data that Xu Yun and Zhou Shaoping are looking for this time.
To describe it with a less rigorous but easy-to-understand example...
If we want to describe and position a point on a plane, the simplest and most appropriate way is to use the XY axis to express its position.
That is (4,2) or (8,3) and so on.
The normalization factor is equivalent to the X-axis coordinate.
After locking the normalization factor, the remaining step is naturally to find the Y-axis coordinate.
Once both "coordinates" are found, the final target can be locked.
Of course.
The actual normalization factor is a description method of probability distribution, which involves combinatorics, so I won’t go into details here.
"The X-axis coordinate..."
In the media live broadcast area, Chen Shanshan repeated the word and asked Zhang Han curiously:
"Dr. Zhang, if the occupancy number operator is regarded as the X-axis coordinate, then what is the Y-axis coordinate that is needed?"
Zhang Han thought for a while 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, second edition of Mr. Zeng Jinyan's "Quantum Mechanics Tutorial", specifically on page 151."
"So in addition to the occupancy operator, they had to calculate 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 following Xu Yun's progress in the audience, also wrote the words "modulus square operator" on the paper and drew a circle.
That's right.
After calculating the occupancy operator.
The next step for Xu Yun and Zhou Shaoping is to calculate the square modulus operator of the 'Pluto' particle.
Or to be more precise...
Angular Momentum.
Students who were particles in their previous lives should know this.
Talking about the properties of a certain particle is actually talking about the characteristics of the Lagrangian quantity of the field of this particle.
This way.
Particle properties can be divided into two types:
Characteristics that can be reflected by the Lagrange quantity, and particle characteristics that are reflected by interactions.
Among them, there are many particle properties that can be reflected through interactions. For example, the most representative one 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, a massless vector field must be introduced to interact with this complex field.
If this massless vector field is an electromagnetic field, the above-mentioned Noether charge is interpreted as an electric charge.
As for the particle properties that can be directly reflected by the Lagrangian quantity of free particles, there are relatively few, and there are only two types in total.
One is the mass of the particle, which is given by the coefficient of the Φ2 term in the Lagrangian quantity.
The second is the spin of the particle, which can be given by the Noether flow of the Lagrange quantity under the spatial rotation transformation.
For 'Pluto' particles.
Currently, no one, including Xu Yun and Witten, can calculate the mass of its particles - because of insufficient information.
But spin is different.
There is a common saying in particle physics that spin is an intrinsic property of particles.
This chapter is not over yet, please click on the next page to continue reading! What does intrinsic mean?
When the police interrogate a person in TV dramas, everyone should have heard this sentence more or less:
"xxx, your nature is actually not bad, you just lack correct guidance. Once you get in, you should reform yourself and strive to become a good person."
The disposition in this sentence is actually the same as the intrinsic nature of particles to some extent. It is an 'innate' attribute and will not be changed by the environment at birth.
For example, a pigeon who writes a novel, although he owes dozens or hundreds of chapter updates, his nature is not bad, he is just a little lazy.
Of course.
This is just a metaphor.
In fact, the intrinsic properties of particles are very complex and involve gauge symmetry.
For example, the chubby Nima next to Xu Yun - let me explain again, this person's name is really Nima, and his English name is Nima Arkani-Hamed.
A few years ago, Nima once said a very famous saying:
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 actually rely on being embedded in a three-dimensional space, so the curvature is its intrinsic property, the square modulus operator is also an intrinsic property that can be calculated mathematically.
As long as the modulus square operator is determined, plus the previous occupancy operator, the probability position of the 'Pluto' particle can be locked.
Or to be more precise.
This is a probability position in mathematics. Whether it can be captured requires actual operation.
If the Jade Emperor is not prepared to give face to the God of the West in his own territory, Witten may end up in vain.
"Xiao Xu."
After deciding to calculate the modulus square operator, Zhou Shaoping pondered for a moment and said to Xu Yun:
"In this way, the derivatives of the spherical coordinate basis vectors with respect to each coordinate variable are left to you, is that okay?"
Xu Yun flipped through the documents and nodded quickly:
"no problem."
After speaking, he paused, hesitated for a moment, and then added:
"Academician Zhou, why don't you also leave the radial and angular decomposition to me?"
What Xu Yun said was not to show off, nor to steal the show, but rather to worry about Zhou Shaoping's health.
Although Zhou Shaoping is younger than Mr. Yang, he is still approaching 90. He has been busy for so long today, and the loss of physical strength and energy is actually huge.
He, a 25-year-old young man, was a little tired at this time. Zhou Shaoping's condition must be worse, but he just kept holding on.
In fact, it's not just Zhou Shaoping.
Except for Nima, a fifty-year-old "young man" at the scene, the remaining Higgs, Tehuft, and Polyakov were all in their eighties or nineties. By this time, their energy consumption was quite high.
.
It's just that the current situation is a group calculation, but it can actually be regarded as a silent battlefield. Everyone represents their own country - for example, Higgs is surrounded by British people and Tehuft's two assistants.
They are all Dutch, and Polyakov's assistant is a bear.
Therefore, although everyone was tired, no one was willing to leave first.
Zhou Shaoping obviously understood this. He thought for a moment and nodded quickly:
"Okay, thank you for the hard work, Xiao Xu."
Hear this.
Mr. Yang, who was opposite Zhou Shaoping, couldn't help but raise his head and glanced at him gently.
Although Mr. Yang stayed abroad for the first half of his life and only returned to China at the end of 2003, he did not have many entanglements or contacts with domestic scientific research factions.
But Zhou Shaoping is also quite famous internationally, so Mr. Yang still knows about his character and experience.
In the early years, Zhou Shaoping had a student he liked very much. He was extremely talented. When he was a sophomore, he was accepted as a disciple by Zhou Shaoping, who had 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 took the initiative to propose the idea of sharing some of the projects 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 excessive magnitude, causing serious damage to the equipment.
In the end, the entire project fell short, and more than 5,000 yuan of funding was wasted.
To know.
That was five thousand yuan in 1983.
At the same time, because the experiment used a first-generation radiation source, the excess radiation directly passed through the longitudinal gradient dipolar magnet, causing the four recent researchers to be exposed to radiation and suffered severe thermal radiation burns.
One of them died three years later, one suffered from extremely severe sequelae in the lungs, and one was blind.
That's right.
This was the accident that happened at the Huairou base, and it was also a very tragic experimental accident in the history of high-energy physics in China.
The blind staff member was Huang Wuxiang, a student of Zhou Shaoping.
Since then.
Although Zhou Shaoping is cheerful and does not lose his temper on weekdays, he has a very strange persistence in research:
He will never leave any tasks that have been assigned to others to be done.
Zhou Shaoping has maintained this habit for 40 years. Unexpectedly, he would actually...
An exception made?
Is it because of lack of physical strength?
Mr. Yang glanced at Zhou Shaoping and shook his head slightly in his heart.
Not quite.
Although Zhou Shaoping did look a little tired, neither his expression nor his calculation efficiency were so bad that he couldn't hold on any longer.
And since it is not due to physical strength, there is only one answer -
Zhou Shaoping met a junior whom he could truly trust. This strong confidence overcame the nightmare in his heart.
Think of this.
Mr. Yang quietly glanced at Xu Yun beside him again, with a slightly subtle expression on his face.
Zhou Shaoping, Zhang Gongding, Hou Xingyuan, Mr. Wang...oh, and Mr. Yang himself.
Unconsciously.
This young man has already had contact with so many academicians of the older generation, and has received their recognition and help. He has high hopes from one old academician after another.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! Looking at the entire younger generation of Chinese scientific circles, Xu Yun is the only one.
But what's interesting is...
He doesn't seem to realize this himself?
............
In fact, if Xu Yun could catch up to this chapter, he might be able to understand what Mr. Yang was thinking through the text.
But unfortunately, he does not have this ability.
So at this time, his mind was not thinking about expectations or trust at all, but was focused on the calculation of data.
After all, this is the final boss.
With Dirichlet's blessing, Xu Yun's mind seemed clear.
Swish swish——
A large number of formulas appeared on the calculation paper one after another with the movement of the pen tip.
The square modulus operator contains both the position operator and the momentum operator, and there is a very precise commutation relationship between the two.
If the particles are measured through phenomena, the derivation is actually very easy, just use a template.
But the problem is that the 'Pluto' particle has never been captured, so the derivation process is very troublesome.
The entry point for Xu Yun's preparation this time is...
Poincaré Group.
Because the Poincaré Group has a very special place:
Its representation can be completely determined by its misdirected subgroup and induced representation.
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 misdirection 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 will not be interfered by other factors.
Well, the above paragraph is in standard Chinese characters and human language.
After a while.
Xu Yun wrote down the eigenstate of operator l^z with eigenvalue m below the secret-level calculation content:
l^ψm=Cψm 1......
At the same time [l^z,l^ ]=l^ we can get l^zl^ =l^ l^ l^z=l^ (1 l^z), so it can be seen that l^ is equivalent to a generating operator, l^?
Equivalent to an annihilation operator.
They make the eigenvalue of l^z always increase or decrease by an integer 1. When the square of the modulus of angular momentum is determined and the maximum eigenvalue of l^z is m=l-1, then there must be l^ψl
=0.
See here.
Maybe some of Zhongzuo Zhou’s classmates feel a little strange:
Why is the maximum 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 determined and l is the maximum allowable value of the quantity m, a state with an eigenvalue of l 1 does not exist.
Since the system can always be in a state where the orbital angular momentum is 0, 0 must be an eigenvalue of the component operator l^z.
It can be seen from the behavior of l^ and l^? that for the angular momentum component operator l^z, the difference between its adjacent eigenvalues is always an integer 1.
Therefore, the eigenvalues of the component operator l^z can only be m=0,±1,±2,...±l-1.
Of course.
Xu Yun's ability to think of this was largely due to the vision he had at this time.
Just like Witten and others ignored the distortion of the lone basis vector before, the state of l 1 is not within the conventional verification range, and there are many more important processes than it.
And if you make a miscalculation here...
So this time's derivation...at least the derivation by the Academy of Sciences team represented by Zhou Shaoping and Xu Yun will completely fall short.
After solving this problem, what remains is the binary spinor.
During this process.
It is necessary to regard the eigenvalue σ of s^z as a variable, then the spin wave function of the particle is a function of σ - as mentioned before, the spin of Pluto particles is a semi-odd number, that is, 1/2,3
/2 or 5/2 etc...
Therefore its matrix factors have only one representation:
ξ′1η′2?ξ′2η′1=(aδ?βγ)(ξ1η2?ξ2η1).
This is a combination of two binary spinors and is a scalar in binary spinor space.
Write here.
Xu Yun flipped through the previous data again.
"It's true...the determinant is equal to 1, which is the real reason why the flux value is too large."
In fact, during the previous process, Xu Yun always felt that there was a doubt that had not been answered:
That is, in the isolated point particle calculation, the expected background is 3.2fb^-1 - this is the data he personally detected, and he detected it more than once.
But the corresponding flux value still becomes larger. Although the phenomenon seems to be due to the influence of 'Pluto' particles, there has never been a suitable explanation in terms of spatial operators.
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 situations, the physical meaning of ξ1ξ?1 ξ2ξ?2 is the probability of finding a particle at a certain point in space.
Therefore ξ1ξ?1 ξ2ξ?2 must be a scalar, that is, it should be:
But for the case of relativity, the physical meaning of ξ1ξ?1 ξ2ξ?2 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 to say, it has only 3 independent actual parameters, and one of them is fixed... Wait!
Suddenly.
The tip of Xu Yun's pen moving on the paper suddenly paused, and a somewhat horrifying thought came to his mind.