Chapter 453: Completely different results (Part 2) (The derivation is over!!)
"..."
At this moment.
Looking at the matrix factors in front of him, Xu Yun's expression was a little subtle.
because......
It's so weird.
Mentioned before.
Although there are still many unsolved mysteries in current particle physics, they are far from touching the essence of the world.
Or to be more precise...
In fact, not only particle physics, there are few fields that are completely understood by humans today.
Not to mention the vast universe, we only understand 5% of the ocean alone, and humans know nothing about the underground world:
The average radius of the earth is 6371 kilometers. The deepest hole dug by humans today is the SG-3 borehole of the Mao Xiongkola ultra-deep drilling hole.
Compared with the radius of the earth, the drilling depth is equivalent to the peel of an apple.
But on the other hand.
Although the depth of the physics community in the microscopic field is relatively limited, some relatively basic concepts are fixed.
For example, an atom is composed of a nucleus and electrons outside the nucleus. In most cases, the electrons are negatively charged, etc...
Another example is a deeper spinor transformation.
The specific calculation process of the spinor transformation is not the focus. After all, many people can't understand it if written... Ahem, after all, it is more complicated and a waste of pen and ink to write.
The key point of this thing is that although it has many processes, the formula corresponding to each process is fixed.
Just like the Coulomb force calculation in high school physics textbooks, just follow the corresponding formula and set the values honestly, without thinking too much.
Of course.
The formula used in the spinor transformation is obviously not the Coulomb force formula, but is called a transformation matrix.
This matrix is a two-dimensional matrix, and the determinant satisfies the following conditions:
det((Ukλ))=1.
For non-relativistic situations, it is also required:
U22=U1?1U12=?U2?1......
That is, (Ukλ)=(aβ?β?a?), and aa? ββ?=1.
The set of all transformation matrices (Ukλ) that satisfy these conditions forms a Lie group, called the SU(2) group.
So the definition of SU(2) group is:
SU(2)≡{U | U∈GL(2,C),U?U=I2x2,|U|=1}......(Some people say character hydrology, explain it here, 8 characters are
A Chinese character, actually I said it once before (I remember)
U? in the above formula is the conjugate transpose matrix of U, so the more specific equivalent definition of the SU(2) group is:
SU(2)≡{(aβ?β?a?)|a,β∈C,|a|2 |β|2=1}.....
See here.
Presumably some smart classmates suddenly understood:
That’s right!
The representation of this matrix factor can only have three independent actual parameters when UkaUβk=det((Uka))δβa=det((Uka))I!
And this situation...
It happens to be the corresponding expression of the second stage in the original 1850 copy reward formula!
Yes.
That path can be divided into three stages, and the first third of the content deduces the Pangu particles...or the copy rewards of dark matter particles.
Not long ago.
After the Jinping Laboratory project ended, I realized the value of the reward.
Xu Yun once deliberately spent some time to dig out the rewards again and study the entire formula.
To be precise, the second stage of the formula was studied.
After all, compared to the first stage, the ‘sense of separation’ between the second and third stages is more obvious.
In other words, if nothing unexpected happens...
The second phase also has an independent outcome...or physical existence.
But unfortunately.
Compared with the relatively intuitive first stage, the second stage is more than ten times more difficult and the content is very complicated.
Even though Xu Yun spent a lot of effort, he could only determine that the second stage described was not a specific probability trajectory, but a very complex scenario.
UkaUβk=det((Uka))δβa=det((Uka))I is the most common mathematical response.
The word scenario can be understood as concepts similar to electric field, magnetic field, etc., but the precision is higher.
If you think of electromagnetic and magnetic fields as ordinary tile houses.
Then the scene in particle physics is equivalent to a well-decorated villa. The requirements in all aspects are very high and all standards need to be met.
all in all.
This is much more difficult than a single probability track.
If we don't find the corresponding theory first, this situation will definitely not be reproduced.
True.
If you use Gauss or Riemann's thinking cards, this part of the content can most likely be cracked. After all, it is the real "god".
But the problem is...
These two thinking cards are really precious, and they are Xu Yun's most critical trump cards.
Whether it is emotion or value, it is not suitable for the second formula - unless this thing can play a particularly big role.
In addition, Xu Yun had to help prepare for today's press conference during that time, so in the end he could only put this matter aside for the time being.
The result was unexpected.
At today's press conference, Xu Yun actually saw the second stage of the response?
Could it be that...
Is that situation in the second stage related to Pluto particles?
If you think about it carefully...
Okay, it seems quite logical.
After all, the first-stage formula discovered Pangea particles, which are standard cold dark matter, and then triggered a series of subsequent misfortunes.
So in the second stage, some unknown things intersect with Pangea particles, which can be said to be completely reasonable and even natural.
Think of this.
Xu Yun's desire to explore suddenly became much stronger.
I saw him straightening his body and quickly starting the next stage of calculations.
Generally speaking,
Both non-relativistic and relativistic transformations of spinors may be needed. In order to distinguish these two transformations, you can add a dot "." to the index of the spinor to indicate that the index obeys the relativistic transformation.
Indicators without "." comply with non-relativistic transformations, that is, the transformation matrix forms a SU(2) group and is subject to equivalent meaning constraints.
Then in this case, just calculate the mechanical momentum and covariant derivative operator of the particle.
Let me tell you something interesting.
The specific calculation process of particle data is actually not much different in principle from the Coulomb force and Lorentz force in high school.
It's just that under the superposition of conditions and frameworks, it turned into another form.
For example, in the equation of motion of charged particles in an electromagnetic field, qUcFac is the four-dimensional force exerted on the charged particles.
This expression includes both Coulomb force and Lorentz force.
It's just that the Coulomb force and Lorentz force here are derived through the principle of least action.
Then add some geodesics, electromagnetic field tensors, proper times, etc., and it will become unrecognizable even if Lorentz is resurrected...
This is the same as the essence of a nuclear power plant is to boil water, but there is a slight difference in expression.
But we have reached this point.
It is not human beings who are responsible for calculating relevant data, but computers.
Xu Yun quickly took out the notebook that the staff had prepared from the table, opened the Aurora System of the Academy of Science and Technology, and entered the calculated data into it.
Xu Yun then arranged for a Laplacian operator for both parties, and then began to find the corresponding regular space.
"The relativistic situation is certain...after all, the speed of light does not change..."
"The magnetic potential has changed, 3.7...4.6...that is, the modes are convergent..."
"The scalar quadrupole moment has a dimensionless parameter...eh?"
After seeing the quadrupole moment scalar data, Xu Yun was stunned.
This particle is a bit interesting...
The modal convergence plus the quadrupole moment scalar has a dimensionless parameter, that is...
In addition to the three quantities of mass, angular momentum, and charge, the other degrees of freedom of the 'Pluto' particle are limited.
See this situation.
The first reaction in Xu Yun's mind was a black hole.
That's right.
black hole.
Students who were in a black hole or were sucked into a black hole in their previous life should know this.
A black hole has only three free observable quantities: mass, angular momentum, and charge. The other physical quantities of a black hole are functions of these three quantities, and there are no other degrees of freedom.
That is to say, all matter entering a black hole will lose all information, leaving only three physical quantities: mass, charge and angular momentum, and all other information will no longer exist.
Therefore, this theorem is also called the three-hair theorem, which means that there are only three "hairs" left: mass, angular momentum, and charge.
The name of this theorem is actually quite elegant.
The Sanmao Theorem was originally called the Hairless Theorem by Wheeler, and the black hole is the "damn little bitch"...
Of course.
This does not mean that matter that only possesses mass, angular momentum, and electric charge is a black hole. Black holes are just a more representative example.
Except for black holes.
There are also particles such as leptons and pions with related properties, but black holes are relatively representative.
Just like when you say 30,000 updates per day, the writer who comes to mind must be the novice fisherman, and then the slightly inferior Ying Ying and others.
Xu Yun then continued to search the data in the aurora system and found that even the dark matter of Pangea particles did not meet the calculated scale.
At present, his state is blessed by Dirichlet, and there should be no errors in the calculation process, so we can only continue to structure it according to the existing data.
So he took a deep breath, regained his composure, and continued to benchmark...
Regular space.
The connected regular space is uncountable, so the relevant index must rely on Urayson's lemma.
That is, any two disjoint closed sets in a normal space can be separated by a continuous function.
A few more minutes passed.
The Aurora system exported a summary item data:
L^2=??2[1sin?θ/θ(sin?θθ) 1(sin?θ)2??2/?φ2]=4.
This seemingly ordinary data is actually an expression of the modulus square operator derived using regularized coordinates.
That's right.
Modulus square operator expression.
That's what I mentioned before...
Y axis data!
At this moment.
As long as Xu Yun reports this data to Zhou Shaoping, and then expands it with the differential operator that Zhou Shaoping is responsible for, he can theoretically complete the calculation of the Fermi surface of the 'Pluto' particles.
Then Xu Yun subconsciously glanced at the two groups of people nearby, Polyakov and David Gross, and found that they were also typing on the keyboard at this time.
This means that they have also entered the final stage and begun their final impact on the Fermi surface data.
At the same time, it is not difficult to see from the calculation paper on the desktop that they still use a limited angle of loss rotation as the entry point.
"..."
See this situation.
Xu Yun frowned subconsciously, and the strange feeling of disobedience in his heart suddenly increased a lot.
This chapter is not over yet, please click on the next page to continue reading! But soon he shook his head gently, bringing his mind back to reality.
Maybe I just think too much.
There shouldn't be any problem with limited angle rotation in theory. On the contrary, the matrix element he chose for the rotation operator around the y-axis is logically a bit far-fetched.
Now that I think about it.
Maybe Zhou Shaoping first considered the idea of limited-angle displacement rotation, but he only agreed to the matrix element direction because he couldn't deny it.
However, it may be a limited-angle rotation or a matrix element of a rotation operator around the y-axis.
At this point, we have reached the final step, and there is no need to think too much about which one is better.
If you hurry up, you should be able to get the answer faster than the other groups.
Think of this.
Xu Yun no longer hesitated and turned his notebook towards Zhou Shaoping:
"Academician Zhou, the expression of the modulus square operator has been published. Please take a look."
Zhou Shaoping moved his laptop, glanced up and down quickly, and nodded approvingly:
"The process is fine. Some of the steps are very clever. He is indeed a genius who can prove Mersenne prime numbers. He is much better than an old guy like me."
Zhou Shaoping's words were not meant to praise Xu Yun, but rather out of emotion.
After all, these days...especially the new generation of physics practitioners, their level of mathematics is generally not particularly high.
There are even fewer who can truly connect the two disciplines.
Among all existing physical directions, the mathematical requirements of astrophysics are relatively high, after all, it involves Riemannian geometry.
Of course.
The so-called low level of mathematics here is the result of comparison with mathematics practitioners, rather than a generalized major.
For a normally graduated undergraduate student in theoretical physics, there is no problem if his mathematics level is lower than that of ordinary people. It is not a concept.
Then Zhou Shaoping took back his thoughts and began to do the final data summary and calculation.
Xu Yun's performance was outstanding, so naturally he couldn't hold back.
Bang bang bang——
Although Zhou Shaoping is over eighty years old, he is very fluent in using computers.
Lines of data were entered by him quickly, and the Aurora system connected to the supercomputer of the Academy of Sciences was giving feedback almost simultaneously.
At the same time, because the laptop screen is in a vertical state, the screen image is parallel to the telephoto and close-up lens hanging from the ceiling and locking the desktop.
So at this point, the camera cannot convey the specific content to the audience.
In fact, it is not just the Academy of Sciences group.
The calculation processes of others such as Polyakov, Tehuft and others are also difficult to see clearly due to perspective problems.
One minute....
three minutes.....
five minutes.....
At the twelfth minute.
Zhou Shaoping suddenly relaxed and exhaled a thick breath.
See this situation.
Xu Yun couldn't help but ask:
"Academician Zhou, are the results out?"
Zhou Shaoping glanced at him and nodded slightly:
"Well, everything went well. The data is consistent with the parameters we calculated. I have sent the specific results to Professor Witten's backend."
Although the telephoto lens loses its imaging effect at this time, the radio and microphone are still normal.
Therefore, Zhou Shaoping's words were quickly spread to the scene and the outside world.
After a while.
In the barrage of major live broadcast platforms, a dense row of [666] flashed through in an instant, and some were [No. 1!]
That's right.
First.
Among the several computing teams on site, Xu Yun and Zhou Shaoping were the first to produce results.
A few more minutes passed.
The Dutch team led by Gerard ter Hooft also obtained the calculation results and sent them to Witten's backend.
Then there is Polyakov...
Anton Salinger.....
Damn...
David Gross.....
Then came Atsushi Suzuki, who was coughing and almost vomiting blood. He was also the last member of the team.
five minutes later.
The person involved in the topic of Witten... and the only scholar who performed calculations independently also moved his fingers from the keyboard.
The atmosphere at the scene suddenly became solemn.
at the same time.
The number of live broadcasts on major platforms has also begun to increase rapidly - this is because the audience has also realized that the results are about to be released, and has invited friends online and offline to enter the live broadcast room.
Then Witten calmly picked up the water glass on the table, took a sip of water, and said something through the headphones.
Half a minute later.
Academician Pan walked out from the backstage again.
However, this time Academician Pan did not go to the first row area, but returned to the podium and said to everyone through the microphone:
"Dear guests and audience, you have been waiting for a long time."
"Now I am very excited to tell you the good news, that is, Professor Witten has gathered the key data calculated by all parties."
"Now we only need to carry out preliminary verification...that is, to eliminate erroneous results, and then we can proceed to the final particle detection."
"The verification process is very simple. You just need to compare several sets of results with each other, and it won't take everyone too much time."
"Now please wait a moment, Professor Witten, you can start."
Academician Pan's last sentence was in English, so simultaneous translation was not needed for Witten to understand what Academician Pan meant.
So soon.
He then came to another terminal device and began to verify the results.
As for Xu Yun, Zhou Shaoping, as well as the scholars and media people present, as well as the audiences from all walks of life outside the venue, they can only wait for the final result with peace of mind.
Even on the live broadcast platform 666, which I had been enjoying for a while, the number of barrages is much less visible to the naked eye.
To be honest.
Everyone was a little nervous at this moment.
Although in terms of ability.
There are a lot of people in China who are better than Xu Yun. Although there are not as many people who are better than Zhou Shaoping as Xu Yun, they are not none.
But at this moment.
Due to many environmental restrictions, this combination of an old man and a young man has become the only representative of the Chinese physics community.
If they miscalculated.
Although it is not too embarrassing to have dark matter as the background, it will be somewhat embarrassing in terms of face and emotions.
It's like the finale of a New Year's Eve dinner.
Some places serve dumplings, some places braised pork with pickled vegetables, some places serve fish with scallion oil, some places serve braised Fujianese, etc...
Tastes and habits may differ from place to place, but the emotion towards the finale dish is the same.
If this dish is missing any year, I will always feel a little uncomfortable.
If you meet some caring and desperate illiterates, you might even accuse this matter of unwarranted charges and call it a scandal or a shame... No, that's wrong, it's a shame.
At this moment.
Even Xu Yun's parents, who were thousands of kilometers away and knew nothing about physics, realized the importance of Xu Yun and Zhou Shaoping's calculation results.
that's all.
Another five or six minutes passed.
Wei Teng, who was comparing the data, suddenly frowned, glanced at Xu Yun and Zhou Shaoping, then turned to Academician Pan and said:
"Mr. Pan, including my personal calculation results, there are a total of eight copies of data in the background."
"Based on the comparison of similar numerical values, seven of them have the same results, one has obvious differences, and this abnormal data comes from..."
"Academician Zhou and the others are in a group."
...
Note:
Let me tell you some good news, there is no mathematical derivation after this chapter.