Chapter 264 It’s Too Early for You

I looked at the clock hanging on the blackboard and saw that there were still a few minutes until the end of the open class.

Xu Chuan thought for a while and said, "There is still a little time before get out of class ends. If any students do not understand anything about what was just taught in class, you can ask questions now."

Hearing this, many students in the audience were eager to give it a try, but they hesitated again when they saw that no one around them responded.

Of course, there must be people who know how to seize opportunities. A Nobel Prize + Philippine Prize winner personally answered the questions. Such an opportunity may be rare once in a lifetime.

Xu Chuan stretched out his hand to signal a student to ask a question, and the student who was hit stood up reflexively.

"Teach Professor." The student who was called seemed not to have expected that he would be so lucky. When he stood up, hundreds of people in the audience were looking at him, and he immediately stammered.

Xu Chuan smiled and said nothing, but quietly waited for the other party to recover.

After taking deep breaths for several times, the lucky man felt relieved and continued: "Well, well, I remember you just mentioned in class that you understood the eigenvectors and eigenvalues ​​of square matrices from the perspective of algebraic geometry. I would like to ask Let’s talk about this.”

"That's an interesting question."

Xu Chuan said with a smile, picked up the chalk from the table again, turned around and wrote on the blackboard behind him: "The eigenvectors and eigenvalues ​​of the square matrix are defined as follows from an algebraic perspective:

"Suppose an n-order matrix A. If there is a number λ and an n-dimensional non-zero column vector x→, so that the following formula is true: Ax→=λx→, then λ is called the eigenvalue of the matrix, and the non-zero column vector x→ is called a matrix, The eigenvector corresponding to the eigenvalue λ.”

"To understand the eigenvectors and eigenvalues ​​of a square matrix from a geometric point of view, the matrix can be regarded as a coordinate system transformation, such as Ax→=λx→, which means that the eigenvector becomes its original value after the coordinate system transformation. λ times, and the extension line of the direction does not change, the direction is the same or opposite."

"At this time, the eigenvectors can be understood as those vectors that remain unchanged under the transformation of the coordinate system, but will be extended by λ times, which is an amplification of this length."

"In addition, it should be noted that there is a corresponding relationship between eigenvectors and eigenvalues. A eigenvector corresponds to a eigenvalue.

When solving the eigenvectors and eigenvalues ​​of a matrix, the eigenvalues ​​are generally found first, and then the eigenvalues ​​are substituted into the equation Ax→=λx→ to find the eigenvectors. "

In front of the blackboard, Xu Chuan wrote the last stroke, turned to look at the student who was still standing, and asked with a smile: "Do you understand?"

The student who asked the question nodded sharply and said excitedly: "I understand! Thank you, professor."

Xu Chuan smiled and then selected students to answer questions.

With the first student taking the lead, students who had hesitated before mustered up the courage to raise their hands, but at this moment, among the hundreds of pairs of raised hands in the entire lecture theater, the probability of being selected was too small.

After answering a few questions, Xu Chuan smiled and said, "The last question is for you. That classmate wearing glasses, what doubts do you have?"

"Professor, can you tell me how you solved the Hodge conjecture?"

The student wearing glasses stood up excitedly and asked, but he did not mention the doubts in the class, but asked another question.

Hearing this question, Xu Chuan was slightly stunned. He did not expect this student to ask such a question, but it was not something that could not be answered.

Smiling, he said with some nostalgia: "Solving the Hodge conjecture was the inspiration I got from Professor Mirzakhani. At the beginning, Professor Mirzakhani once left me a manuscript. By studying that manuscript, I I unexpectedly found some solutions to Hodge’s conjecture.”

"As for the specific process"

After a pause, Xu Chuan then smiled and said: "This cannot be explained in one or two sentences, and for you guys now, it is too early to say this."

"Based on your current foundation, I am afraid that the vast majority of people cannot even fully understand the true meaning of the difficult problem of Hodge's conjecture. As for my proof paper, there is no need to think about it, even if I am here to explain it today I’m afraid more than 99% of the people present can’t understand the report.”

"For this kind of conjecture, which is considered top-notch in the current mathematics world, I suggest that you proceed step by step. First lay the most basic things, try to break through your own boundaries, and then move towards your goals and ideals step by step. struggle."

"As for now, it's still a little early for you."

Xu Chuan did not talk about how he solved the Hodge conjecture. As he said, it was not contempt or contempt, but for the students sitting in this classroom, it is really too early to talk about this now.

Not everyone is a genius like Terence Tao or Schultz, who can have extremely high attainments in mathematics at the undergraduate or graduate level.

As soon as he finished speaking, someone asked: "Professor, can you tell me what you are researching after returning to China? Physics, mathematics, or astronomy? I think many people are very interested in your research direction, including We are also quite curious.”

Xu Chuan thought for a while and said with a smile: "NS equations and particle physics, I am mainly studying these things during this time."

He did not reveal his actual research in this class, but just found a reason to talk about it. Some things can be announced after completion, but the process still needs to be kept confidential.

"Ring ring ring ring."

When the bell rang, Xu Chuan put away the textbooks he brought with him and left without even turning off the projection equipment.

There were so many students here that if they were blocked, they would not be able to leave for a while.

After all, it was the first class and these students were quite enthusiastic, so the best strategy was to run away before they could react.

When there were more classes in the future, the students would get used to it and would not have to worry about being blocked in the crowd.

There was still a big difference between college students and those fanatical fans. The former would still be embarrassed to save face, but as for the latter, there was no need to say more.

There were things like sneaking into their idols' homes to steal underwear and personal belongings, and rushing onto the stage like crazy.

Strolling all the way, Xu Chuan came to Chen Zhengping's office.

He knocked on the door and heard a voice from inside asking him to come in. He pushed the door open and walked in. To his surprise, there was not only his tutor Chen Zhengping in the office, but also Liu Gaojun, the president of Nanjing University.

"Teacher, president." Xu Chuan smiled and greeted.

"Professor Xu is here, please take a seat." Principal Liu greeted him with a smile: "How do you feel about your first class at NTU?"

Xu Chuan smiled and said: "It's pretty good. The students are very serious and enthusiastic."

"Hahahaha, only you have this charm." Liu Gaojun laughed: "If there is anything you are not satisfied with, or any suggestions on teaching, you can tell me, and the school will try its best to find a solution."

Xu Chuan nodded and smiled: "Of course."

Aside, Chen Zhengping interrupted and asked: "The data analysis you sent to my email a few days ago, is it the experimental data of the ALICE detector?"

"Well, before the New Year and during the Chinese New Year, I analyzed the experimental data of the ALICE detector. Thanks to your help, I found some abnormal signals and data from it."

"It has been sent to Witten and CERN. I hope they can do a few sets of collision experiments to see if the analysis results can be verified."

Chen Zhengping pondered for a moment, and then said: "Do you think that is the performance of inert neutrinos?"

As soon as Xu Chuan sent the analysis data and the Daritz diagram to his email, he saw it.

Although he was surprised at the speed of his student's research, he still studied and analyzed these Daritz diagrams seriously.

From the image, it can be seen that there may be a new particle in the data analyzed by Xu Chuan, and the probability is not small.

But it is only possible, and even if there is a particle, it is not necessarily an inert neutrino.

Although his research focus has now shifted to material physics, he is a high-energy physics and condensed matter physics graduate after all.

Moreover, he has never stopped studying high-energy physics and particle physics. He goes to CERN every year to participate in research and data analysis, and keeps an eye on the cutting-edge information in these two fields.

Inert neutrinos are not particles in the standard model.

In the current theory of physics, inert neutrinos are a type of dark matter, and the current physics community has never found any trace of dark matter. All theories are based on the movement of celestial bodies, the phenomenon of Newton's universal gravitation, the gravitational lens effect, the formation of large-scale structures in the universe, microwave background radiation and other observation results.

For Chen Zhengping, although he believes that dark matter exists, he does not believe that today's technology can observe dark matter.

Unless all aspects of the Large Hadron Collider are upgraded on a large scale, it is almost impossible to detect the existence of dark matter with the current collision energy level and the observation level of the detector.

So even if there is a new particle or some undiscovered phenomenon in the experimental data of the ALICE detector this time, Chen Zhengping does not think it is an inert neutrino.

In the office, Xu Chuan nodded and said, "Yes, I think it is very likely to be an inert neutrino."

Chen Zhengping asked, "Have you considered the probability that this is an antineutrino?"

From Xu Chuan's analysis results, he felt that this might be an unknown neutrino or an antineutrino particle.

The so-called antineutrino particle is not antimatter, it is another state of neutrino.

The spin direction of neutrino is opposite to the direction of motion, while the spin direction of antineutrino is the same as the direction of motion.

The nature of their interaction with matter is different. Neutrinos are only left-handed and antineutrinos are only right-handed.

It is the hypothesis of the existence of neutrinos proposed by Austrian physicist Pauli. In 1965, two physicists, Cowen and Rhines, produced antineutrinos using beta decay of nuclear reactor products and observed them.

So theoretically, it is also possible that they are produced in the Large Hadron Collider.

Xu Chuan said: "I have considered it, but theoretically, the probability that it is an unknown neutrino or antineutrino is much lower than the probability that it is a sterile neutrino."

Hearing this, Chen Zhengping quickly asked with interest: "What do you mean?"

He still has some understanding of this student. If there is not enough evidence, this student will not easily say such a thing.

Since he said that the probability of sterile neutrinos is higher, he must have some evidence in his hand.

If it is really confirmed that traces of inert neutrinos were found in the experimental data of the ALICE detector, it would be a super-large nuclear bomb for the entire physics community, even the entire scientific community, and even the entire society!

After all, inert neutrinos are one of the warm dark matter particles that constitute dark matter from the current theory.

If it is confirmed, the discovery of dark matter will become the most sensational news in the physics community and even the scientific community this year.

Xu Chuan pondered for a moment, sorted out his thoughts and said: "From the Daritz diagram I made, we can clearly see the energy level trajectory of this new particle. It presents a ︺-shaped arc, which is completely different from all conventional particles."

"Even the kinetic energy trajectory of neutrinos and antineutrinos on the Daritz diagram will not show this, so it is most likely a new type of particle, and its performance characteristics are not included in the conventional standard model particles."

"Secondly, I don't know if you have noticed that in all the Daritz diagrams, the data representing this unknown new particle are all intermittent."

"This means that the experimental data observed by the ALICE detector is actually not perfect. It can only detect and record part of the resonant state structure that this unknown particle can show."

"And the inert neutrino is theoretically part of the warm dark matter in dark matter. Theoretically, warm dark matter does not participate in strong interactions, otherwise Then the process of primordial nucleosynthesis will be disturbed, the abundance of light elements will change, and it will lead to inconsistency with current observations. "

"In the large intensive particle collider, the existence of primordial nuclei can be ubiquitous. In this case, only when sterile neutrinos synthesize warm dark matter and obtain excess abundance from the thermal decoupling mechanism can they be observed by the ALICE detector. From this point of view, there is no doubt that it meets the requirements. "

"In addition, weakly interacting massive particles (WIMPs) are one of the most widely discussed dark matter candidates. They refer to some stable particles with mass and interaction strength near the electroweak scale, which obtain known excess abundance through the thermal decoupling mechanism."

"In the standard model of particle physics known to mankind, there are no particles that meet these properties at the same time, which means that the particles that produce this property must be new physical particles beyond the standard model."

"From the above viewpoints, the probability that this new type of particle is a sterile neutrino is quite large. "