Witten, who had just sorted out a document and was about to continue calculating according to the existing plan, subconsciously stopped what he was doing.
Then he raised his head, adjusted his glasses slightly, a trace of doubt flashed across his face, and asked Xu Yun:
"Dr. Xu, do you... have any ideas?"
Xu Yun glanced at Zhou Shaoping, who had a slightly worried look in his eyes, nodded, and said:
"There is a problem."
"you say."
Xu Yun stretched out his hand and pointed at the computer in front of Witten:
"Professor Witten, I think some of the links we preset before seem to be a bit poorly thought out."
"Thoughtless?"
Witten raised his brows and tilted his head slightly to the left. This was his habitual action when encountering problems:
"Dr. Xu, what do you mean?"
Xu Yun walked quickly to his side, and the chubby little girl moved her position wisely, revealing a small gap for Xu Yun to stand.
"I thank you Nima."
Xu Yun first politely thanked Nima, then picked up the stylus and marked a few more places on the screen:
"Professor Witten, look here... and here, these two places."
After Xu Yun has drawn the area.
Witten poked his head forward and examined it carefully.
The first regional content drawn by Xu Yun is a static wave packet formula:
I think the smart classmates Zhou Zhou have already figured it out.
That’s right!
The second term of this formula is a radial oscillating radiation flow, while the first term is a tangential surrounding flow around the polarization direction n.
In other words.
This is a mathematical description of the spin of a particle.
Under this formula.
A particle with spin, whether it is a boson or a fermion. In addition to the change in speed under the Lorenz transformation, there will also be a jump in magnitude at its conserved charge center or center of mass.
This jump can be fed back into a mathematical expression, thereby correcting the covariance of the 'Pluto' particle.
Considering that it is difficult for some students to understand, here is another really well-known concept:
Shrinking effect.
The shrinkage effect is a special relativistic effect, which is a distortion caused by the oppression of space by a mass body.
In human words, when viewed from an external reference system, the length of a moving object in the direction of motion shrinks.
for example.
In a closed space that moves in a straight line - let's say a car.
There was an unknown classmate sitting in the car. He was bored and threw an apple vertically.
So from the moment the apple is thrown to the moment the apple returns to the throwing point, the apple moves vertically twice between the two moments, that is, vertically rising and vertically falling.
between two moments.
The total distance of the apple's motion is the sum of the two vertical motion distances.
But this happened in the car.
From the perspective of a person standing still outside the car, the distance the apple travels between the time it is thrown and the time it returns to the point where it was thrown is a parabola.
Since the length of the curve between the two points is greater than the length of the straight line, that is to say, from the perspective of a person standing still outside the car, the total distance traveled by the apple during the throw and return process is greater than twice the vertical distance of the apple's vertical lift.
At the same time, regardless of whether there are people inside or outside the car, the measurable throwing speed of the apple is the same.
Otherwise there would be energy created out of nothing.
Ever since.
Calculated according to "time equals the ratio of distance and speed", people outside the car will feel that the time it takes for the apple in the car to go from being thrown to returning is longer than the vertical lift of the apple.
In other words, from the outside of the car, the time inside the car was extended during this exercise.
This extended time increment is caused by the shortening of the length of the car along the direction of motion as seen by outsiders.
The faster the car runs in a straight line, the longer the usable time in the car seen by people outside the car (that is, the slower time passes), and the shorter the length of the car.
That is to say, the closer to the speed of light, the more obvious the shrinkage effect. (It is recommended to insert an eye here to avoid getting lost in a certain plot in the future)
It can also be seen from this that the theory of relativity does not completely reject the existing results of classical physics.
It just breaks through some of the limitations of the era in understanding classical physics.
all in all.
To a certain extent, the shrinkage effect is a reflection of the expansion of this formula to another level - note that it is to a certain extent.
It plays a very important role in the special theory of relativity and belongs to the category of "base".
So the same logic.
The wave packet formula drawn by Xu Yun can also be understood as a very important tool in the process of searching for 'Pluto' particles.
Once something goes wrong with this tool, the consequences will be unimaginable.
Think of this.
Wei Teng couldn't help but look up at Xu Yun beside him.
He didn't speak, but once again focused on the words circled by Xu Yun...
In the second area.
The calculation content in this area is relatively complicated, with more than ten lines, which seems quite dazzling.
They involve characteristic subspaces and chiral operators, which are represented by 4 basis pairs in the spinor space C^4, corresponding to the Dirac matrix.
This characteristic subspace is the so-called left/right-handed spinor, so that a Dirac spinor can be written as the direct sum of left/right-handed spinors.
As we all know.
When considering that the Dirac matrix acts on a 4-spinor, it is actually the corresponding Pauli matrix acting on a 2-component left/right hand spinor.
The eigenvalues of the Pauli matrix are all {1/2,-1/2}, which can be used to describe the algebraic properties of 'Pluto' particles.
Use real-life examples to illustrate.
The two areas drawn by Xu Yun are like the sonar and positioning software of fishing boats, two core tools essential for fishing.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! The positioning software can help the boat owner find the suitable fishing direction - such as XX degrees east by west, etc.
Sonar can further locate the fish after arriving in the area.
If these two tools have problems as Xu Yun said...
Then a situation will arise:
The fishing boat was navigated in the wrong direction. After a long time of sonar detection, it only detected the hook hanging by the fisherman in the sea, but nothing else was found.
This way.
The consequences can be imagined.
As a top smart man in the world, Witten quickly realized the seriousness of this matter.
However, these data are important, which does not mean that there must be problems if they are circled. There is no inevitable connection between the two.
Just like nuclear weapons are equally important, but you go to the door of the relevant department and say that tomorrow all nuclear weapons around the world will explode?
Therefore, if Xu Yun wants to confirm that his guess is correct, he needs to come up with more intuitive evidence:
"Dr. Xu, is there something wrong with the data in these two areas?"
Xu Yun was obviously prepared for this, and quickly circled the values of the shielding constant σ, and the single particle configuration n, l, ml, ms8.
Then he took a deep breath, organized some words, and said to Witten:
"Professor Witten, you should know that according to the Pauli exclusion principle, the multi-electron wave function must be exchange antisymmetric - we have now extended this principle to other particles."
"That is, when multiple particles interact, their wave functions must also be exchange antisymmetric."
Witten nodded:
"yes."
Xu Yun paused and then said:
"At the beginning of the calculation, our method is to introduce an additional central field approximation and treat the effects of other particles on a single particle as a spherically symmetric mean field."
"This is equivalent to some particles having a certain shielding effect on the target particles, so values such as shielding constants are derived."
"But have you ever thought that multi-particles may undergo distortion of the lone basis vector under certain circumstances, making the values n, l, ml, and ms8 meaningless?"
"For example, Σ1241 hyperons, Ω2470 baryons, etc. Although there are very few particles that meet the conditions, this situation does exist."
"This is like a ship's navigation system being affected by external forces. The navigation software can still be logged in, but it has essentially expired..."
"We currently know very little about 'Pluto' particles, so theoretically this possibility should exist..."
Hear this.
Witten...no, to be precise, including Nima, Zhou Shaoping, Hu Teft...
Even everyone, including Mr. Yang and Higgs, were immediately stunned.
Distortion of solitary basis vector?
this......
Xu Yun's words silenced everyone at the scene for more than ten seconds.
After regaining consciousness.
Witten and Hutft subconsciously looked at each other without any communication. The two of them flipped through the documents on the table at the same time.
Followed by Zhou Shaoping, Nima, David Gross and others...
Even Mr. Yang and Higgs couldn't help but stand up from their seats and came to Witten's side with Polyakov's help.
About half a minute passed.
Witten closed the folder and quickly started calculating on the math paper.
Another five minutes passed.
Witten's pen tip suddenly paused, he was silent for a moment, and he let out a sigh of relief with emotion on his face.
He raised his head, looked at Xu Yun, and said slowly:
"Dr. Xu, you are right, we made a fatal mistake."
Students who have taken advanced physics should know this.
The shape of orbits in textbooks can be expressed by wave functions.
However, the wave function is a complex number, and complex numbers have imaginary parts—this refers to particle orbits, not hybrid orbits.
Therefore, the current common way to optimize the wave function is to take the modulus, but this method has a very fatal feature:
It will lose some degenerate information.
For example, for the Σ1241 hyperon, the result is the same if its m is plus or minus 1.
But m refers to mass, how can mass be negative?
As a result, the wave function spatial distribution of the upper and lower components of the spinor wave function will be different.
Mentioned before.
A theory that has no problems in mathematics may not necessarily become axioms in physics, such as M theory.
However, a theory that conforms to reality in physics must conform to mathematics. No matter how bad it is, it will not conform to mathematics for the time being, but it will definitely conform to mathematics in the future.
Therefore, for those particles that lose part of the degenerate information.
When they lead to irreversible misunderstandings in the field of mathematics, another framework must be used.
However, under normal circumstances, this special particle is very rare.
Currently, there are only seven particles including subatoms that can cause this situation:
N1675.
Σ1241.
N1880.
Ω2380.
Ω2470.
△2200.
And Pc4457.(See pdglive official website)
Although the current number of basic particles is only 61, it can be divided into a large number of branches based on decay parameters and pole structures:
For example, there are 23 kinds of ∧hyperons, and the number spans from 1380 to 2585.
There are eight kinds of baryons to which ∧hyperons belong.
For example, N, Ω, △, etc.....
These subatomic particles are scattered and added together, and the total number is 9643. This is the official data of CERN. You can check it by searching pdglive.
Therefore, when time was relatively tight, Witten and others subconsciously ignored this small probability situation.
This is not to say that they are incompetent or careless, but that there are too many issues to consider, and the priority of this low-probability situation is very low.
For example, spin has been mentioned many times before, such as the state of spatial angular distribution... These are all details that need to be taken into consideration.
In fact, not only Witten, but Xu Yun himself was also confused.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! He didn't think about this detail at all at first. He was thinking about whether he could start with the identity effect and try to calculate some properties of the unknown particle.
I don’t know what happened as a result.
For a short period of time, his mind felt as if he could not think of anything else, except for the deformation of the lonely Motoya.
Maybe this is the legendary flash of inspiration...
all in all.
Although this oversight is not that obvious, it is almost fatal.
Fortunately, Xu Yun warned him, otherwise the consequences would be really disastrous.
Think of this.
Wei Teng quickly cast a grateful look at Xu Yun and held his hand heavily:
"Thank you so much, Dr. Xu Yun!"
Xu Yun smiled modestly:
"Professor Witten, you're welcome. This is what I should do. Our time is limited, so let's try to solve the problem first."
Witten obviously understood that time was tight, so he decisively let go of Xu Yun's hand.
But in the one second before letting go, he exerted a little force on his palm, and everything went without saying.
Then Witten pondered for a moment and turned to look at Higgs:
"Mr. Higgs, I may need a favor from you now."
Mentioned before.
Higgs himself won fame and the Nobel Prize for the Higgs particle, but the essential reason for his honor was actually the discovery of the Higgs mechanism.
The Higgs particle is only a proof of the Higgs mechanism, and technically the latter is obviously higher.
When there is a problem with one of the eigenstate frameworks, Higgs is naturally a worthy candidate to fix the leak.
In the words of the Internet, it is a professional counterpart.
Higgs, who is now 93 years old, is only seven years younger than Yang. He is also not in particularly good spirits and seems a bit irresponsible.
But after hearing Witten’s request.
Higgs still cheered up a lot, came to the table, picked up a pen, and started calculating seriously.
Witten's mistake mainly lies in the loss of some degenerate information, but there is not much problem with the basic data.
The first value represents the angular frequency, and the subsequent one is the optimization of the real part, which perfectly optimizes the wave function of these special particles. (Refer to Weinberg's notes, which were compiled and published after his death. If Weinberg
Ge did not pass away, I actually wanted to arrange for him to write it in his own hand)
Then Witten and others put their heads together to study the formula for a few seconds, and Zhou Shaoping suddenly let out a light sigh:
"Eh...if calculated according to this modified configuration, the base of the 'Pluto' particle is easy to determine, but its iso-energy surface in the momentum space seems to be a little difficult..."
Equienergy surfaces of momentum space.
This is the so-called Fermi surface.
The Fermi surface was first defined in the ideal non-interactive Fermi gas system, and was later extended to electronic models. In recent years, it is commonly used in the field of solid materials.
Such as semiconductors.
The actual energy state structure of a semiconductor is the energy band given by the perturbation of the periodic potential field, such as the valence band, conduction band, etc., where the electrons are filled.
For semiconductors, the valence band is almost filled, and the highest filling position is the top of the valence band.
At the same time, based on the number of particles, the Fermi surface can be determined.
However, this concept is also applicable to some high-energy physics frameworks, because its essence is the movement of free electrons in a three-dimensional infinite potential well.
The electron corresponds to λ=h/p, so a standing wave is formed in the conductor.
Then according to the definition of wave vector, the wave vector value of the standing wave in which a single electron is located can be determined.
So this thing also conforms to a distribution called the Fermi Dirac distribution, which belongs to the category of wave-particle duality.
All current particles possess wave-particle duality, even the 'Pluto' particles are no exception.
Therefore, it is not an easy task to define the Fermi surface of the 'Pluto' particle, that is, to lock the dividing area between its occupied and unoccupied states.
Of course.
In many cases, difficulty and reward are equivalent.
If the framework of Higgs correction is [Positioning System] and [Sonar].
Then the iso-energy surface of the 'Pluto' particles in the momentum space is equivalent to a large fishing net for fishing.
Navigation direction and the location of fish schools are the basis of fishing. If you want to really catch the fish, you can’t do it without a fishing net. This sentence is actually more in line with the current situation in reverse.
In other words, fishing will be much easier with a fishing net.
Then Witten flipped his wrist and looked at his watch.
At this time, there are still three hours and five minutes before the final time limit given by the Chinese Academy of Sciences.
"Everyone."
At this point, Witten's originally gentle face also showed a little excitement and ruddy color:
"As you can see, so far, our mathematical calculation results are actually completely consistent with the theoretical model - especially after optimizing a new configuration."
"So I would like to ask you to work harder and try to calculate the Fermi surface data of that particle within two hours. Please!"
Witten's words were clearly recorded by the radio equipment and spread. After a 15-second delay, they spread to all live broadcast rooms at home and abroad.
Hou Xingjian, who was in the background, couldn't help but smile at Academician Pan beside him and said:
"Xiao Pan, this Witten... he is a real genius."
Academician Pan also nodded in agreement.
Witten's words did not conceal the request in his tone at all. He seemed to have a very low posture. If he added a khaki, he would have thought he was a craftsman from Neon.
But for Zhou Shaoping, Nima, Higgs and others opposite him, this move also put them in a high position:
I said this in public, you have to give me some face, right?
In addition, if the 'Pluto' particle really exists, its influence on the physics world will probably be second only to dark matter:
Judging from the many current properties, the 'Pluto' particle is definitely special in some aspects - assuming it really exists.
Therefore, it is difficult for these big guys to refuse due to emotions and reasons.
in addition......
Although Witten's words were aimed at all the big guys in the first row.
But the people he was facing were Zhou Shaoping and Yang Lao. This move can be said to have given the Chinese physics community a good reputation.
Otherwise, how could Hou Xingyuan say that others are smart? He was able to come up with the optimal solution in this situation, and he didn't make others feel bad at all.
I can only say that he is worthy of being a person who has participated in the presidential campaign team...
In addition to Hou Xingyuan, those who realized this also included Yang Lao and Zhou Shaoping.
only......
Today's Mr. Yang obviously does not have the physical condition to take action.
Although Mr. Yang is over a hundred years old, his thinking is still clear, but his calculation skills and physical strength are no longer what they used to be.
The previous few hours of sitting and verifying the lux value and exponential mapping generator had consumed almost all of Yang's energy and physical strength.
Therefore, the only one who can "fight" on behalf of China at this time is Zhou Shaoping.
Think of this.
Zhou Shaoping couldn't help but take a deep breath, whispered a few times to Mr. Yang, then turned his head to his side and said in a longer voice: