Great Country Academician

Chapter 532 NP=P Conjecture

Although it is a pity that the technology on the Wukong dark matter detection satellite has not been applied to the Large Strong Particle Collider, Academician Chang Jin's words gave Xu Chuan enough reminder to remind him of something else.

When he was doing experiments at CERN in his previous life, the data he found for the discovery and detection of sterile neutrinos was incomplete.

Of course, this incompleteness does not mean that it is insufficient to verify the existence of sterile neutrinos and dark matter.

But the information about these particles is still the same as the discovery of sterile neutrinos in this life, with a small part of it uncertain.

If we say that the discovery of sterile neutrinos at European Atomic Energy a few years ago only found the properties of the particles in the normal state, and the remaining dark matter properties were not detected at all;

So in my previous life, I saw some of the properties of dark matter and could judge that it belonged to dark matter, but it was not comprehensive.

It's just that at that time, he and many physicists were so excited about this great new continent and new century that they couldn't help themselves, and they didn't pay too much attention to these details.

Now that I think about it carefully, this is probably related to the detector technology of CERN's upgraded high-brightness LH-LHC collider.

As Academician Chang Jin said, the observation of dark matter and dark energy by collider detectors is mainly based on searching for the energy and momentum loss signals generated by dark matter during annihilation and decay.

Perhaps CERN in a previous life took exactly this route when upgrading and optimizing its detectors.

This was so that when he discovered and searched for dark matter, he could only confirm part of the information.

Because theoretically speaking, the annihilation of dark matter produces charged particles (mainly positron and negative electron pairs, neutral neutrinos, photons, and charged particles, etc.).

The signals generated by these particles will cover the entire electromagnetic band, and there are two main types of signals.

One is the synchrotron radiation of charged particles in the local magnetic field, which is in the radio observation band;

The other is the inverse Compton scattering of high-energy electrons and CMB photons. The scattered photons are generally in the X-ray band.

Due to uncertain factors such as dark matter particles, dark matter density profiles, and magnetic field environments, dark matter

Indirect detection requires the integration of multi-band characteristics before it is possible to give further restrictions on dark matter.

Therefore, the collider that mainly searches for the energy and momentum loss signals generated by dark matter during annihilation and decay cannot theoretically see the full picture of dark matter.

Moreover, dark matter does not participate in electromagnetic interaction, does not participate in strong interaction, or does not carry electric charge and color charge.

Therefore, its main component cannot be any particle in the standard model, nor can it be a black hole formed by the collapse of a star. It is a substance that has never been discovered.

Dark matter requires properties such as stability, no charge, and weak interactions. Therefore, most of the elementary particles in the standard model of particle physics cannot constitute dark matter.

If possible, the only ones among regular particles would be neutrinos.

However, because neutrinos can only constitute so-called hot dark matter, which is inconsistent with observations of the large-scale structure of the universe, conventional neutrinos have also been excluded.

The particles that constitute dark matter must be new particles beyond the standard model.

The sterile neutrino he discovered does not belong to the regular neutrino form, so it is a type of warm dark matter.

However, even if the sterile neutrino does not belong to the regular neutrino, it still has some material properties in the regular state category.

Using this, theoretically speaking, he can forcibly annihilate the sterile neutrinos through collision control of the high-energy collider to form two other particles, thereby observing various information such as its mass.

Perhaps he knows where to reconstruct the collider detector.

Thinking of this, Xu Chuan's eyes suddenly brightened.

He knows what to do!

Across the way, while Xu Chuan was deep in thought, Academician Chang Jin took a sip from his teacup.

From the state of Xu Chuan opposite him, it was obvious that he had some thoughts and was thinking about it, so he didn't bother him and waited quietly until he came back to his senses.

Looking at Xu Chuan with an excited look on his face, Chang Jin smiled and asked curiously: "Does Academician Xu have an idea?"

Xu Chuan nodded and said with a smile: "We do have some theoretical ideas, but they still need to be improved. As for whether they are useful, we may have to wait until the collider and detector are all prepared before we can know."

Regarding unestablished scientific research theories, no matter how confident he is, he will not speak out with too much certainty.

Just like many people in the academic community believe that the papers he posted on arxiv can be viewed as formal journal papers. No matter what the outside world says, he never thinks that he will not make mistakes. All the papers he publishes are correct.

Especially at his current height, the more critical the research, the more cautious he must be in his words and deeds.

On the opposite side, after hearing what Xu Chuan said, Chang Jin had a look of interest on his face and asked curiously: "If it's convenient, can you talk to me?"

Xu Chuan smiled and said, "What's the inconvenience? Speaking of which, this inspiration was given by you, Academician Chang."

After a slight pause, he collected his thoughts and then continued: "Similar characteristics were clearly seen in the previous sterile neutrinos. However, compared with theoretical dark matter, sterile neutrinos have some additional rules. State attributes.”

"Therefore, by using these characteristics, tracking them, and then judging that dark matter can transform into two other particles under high-energy collision conditions, through continuous experiments, we can figure out and deduce the nature of dark matter bit by bit. Dark'nature."

"However, theoretically speaking, it is very difficult to accurately determine the data of sterile neutrino collisions during the collision of high-energy particles. This may require trillions or more collisions before we can Find that one useful clue.”

After listening to Xu Chuan's explanation, Chang Jin thought for a moment and then said: "According to this idea, enough collision data may be able to completely search for dark matter particles, at least complete information about sterile neutrino particles. .”

"This is definitely a groundbreaking discovery for the world of physics."

"It's just that to do this, you have to create sterile neutrinos first, and find a way to make them collide in the collider, and you have to eliminate the impact of collisions with other particles."

"This level of difficulty is not ordinary."

As the chief scientist of the Dark Matter Particle Detection Satellite, he can easily understand this new method.

Theoretically, it is indeed feasible, and more comprehensive data can be collected, but the difficulty is really not that great.

Whether it is finding a way to create sterile neutrinos, guiding them to collide in a collider, or eliminating interference from other particles, it is not easy, and it can even be said to be as difficult as climbing to the sky.

Xu Chuan said with a smile: "If we can observe the complete information data of sterile neutrinos, no matter how much we pay and no matter how difficult the problems we encounter, it will be worth it."

After chatting with Academician Chang Jinchang about various particle detection technologies for a while, Xu Chuan couldn't wait to return to the office.

He already has a general direction for the exploration of dark matter.

The next work is to improve it as much as possible theoretically.

I hope he can successfully solve this work before the High Energy Physics Conference held by the Physical Society.

The days passed like this day by day.

The time soon came to mid-to-late May.

These days, Xu Chuan has not gone to Xinghai Research Institute again.

For more than half a month, he devoted himself to perfecting the theoretical basis for the detection of sterile neutrinos and dark matter at NTU.

".With the help of quantum field theory, the change rate of particle number density in co-moving volume a, 1/ad/dt(n1a)=∫···∫∏j=1(dpj/(2π)δ+(pj-mj) )((2π)δ(p1+p2-p3-p4)∑”

"In the co-moving volume, the particle number density will not be diluted with expansion, and the right side of the equation can be divided into two parts, in which the dark matter particles produce the scattering cross section of the annihilation process, 1/ad/dt (n1a) = ∫···∫∏ j=1(dpj/(2π)δ+(pj-mj))”

"P is the momentum of each particle participating in the scattering process, |M| is the scattering amplitude."

"The second part is the equilibrium statistical distribution of the energy of each particle."

"That is: the change rate of dark matter abundance is equal to the difference between its production cross section and annihilation cross section. The physical meaning of the cross section is the probability of the reaction occurring."

"."

Lines of calculations were written down in Xu Chuan's hands.

For the exploration of dark matter, the Boltzmann transport equation is a very important part.

It describes the evolution law of dark matter particle abundance Y with "mass-to-temperature ratio" x. The parameters in the equation are determined by specific particle physics models.

And if you want to find the required data from countless collision information data, it is completely impossible to do it with human power alone.

At this time, the importance of mathematical tools is fully reflected.

As long as the lowest-level calculation formula can be produced, mathematics can completely use computers and software to establish a mathematical model, and use mathematical models to find the required piece of data from trillions of pieces of information.

The signature pen in his hand touched down the last symbol. Xu Chuan put down the pen, breathed a long sigh of relief and stretched.

After spending more than half a month, he finally perfected the ideas in his mind and formed a set of logical and self-consistent theories, as well as a set of calculations from many parameters to calculate the collision and annihilation of inert neutrinos. The basic formula of the mathematical model of transformation particles.

All that's left is to transform these theories into actual equipment and mathematical models.

Looking at the manuscript paper in his hand, the corners of Xu Chuan's mouth curled up.

It seems that I have to trouble my senior sister again.

At the foot of Purple Mountain, under the Chuanhai Network Technology Co., Ltd. building not far from Chuanhai Materials Research Institute, Xu Chuan found Liu Jiaxin who was busy working in the office.

With a smile, he knocked on the door.

In the office, the senior who was studying something was woken up by a knock on the door. She looked up and was obviously stunned for a moment when she saw him, and then a smile appeared on her face.

"How did you come."

Xu Chuan walked forward and said with a smile: "Let's take a look at you."

Hearing this, Liu Jiaxin's earlobes suddenly turned red. Xu Chuan didn't notice it. He said with a smile and his eyes fell on the desk.

On it, there were dense calculation formulas on the scattered manuscript paper. His good eyesight allowed him to clearly see some of the mathematical formulas on it, which looked familiar.

Glancing at the manuscript paper, he asked curiously: "Are you studying mathematics?"

Liu Jiaxin nodded, tucked a strand of hanging black hair behind her ear, and replied: "Well, I want to see if I can solve some mathematical problems in artificial intelligence."

For artificial intelligence, the underlying logical algorithm is undoubtedly inseparable from mathematics.

Although Princeton's computer science department is not among the top, its mathematics field is something that no other college can catch up with.

Hearing this, Xu Chuan immediately became interested: "Let me take a look?"

Liu Jiaxin nodded, sorted the manuscript paper on the table and handed it over.

Xu Chuan took the manuscript paper and started reading it.

"A large integer factorization algorithm based on factorization basis."

When he saw the title on the manuscript paper, he was stunned.

This title?

After thinking for a while, Xu Chuan suddenly raised his head, his eyes fell on the senior sister's face, he couldn't help but swallowed and asked: "Are you studying the NP=P conjecture?"

No wonder when he glanced at it before, he always felt that the formula on the manuscript paper looked very familiar.

The factorization problem of positive integers is part of the seven millennium puzzles NP=P conjecture.

To be honest, he really didn't expect Liu Jiaxin to be studying this aspect.

Because for the mathematics community, there are many things related to the field of artificial intelligence.

Whether it is linear algebra, calculus, probability theory, statistics or discrete mathematics, they all affect the lowest level logical algorithm of the computer.

But if you want to say that the most critical and influential one is definitely the NP=P conjecture.

It is the only one of the seven millennium problems related to computer science. Its status in the world of mathematics and computer science goes without saying.

Of course, it goes without saying that it’s difficult.

Being stared at by Xu Chuan's fiery eyes, Liu Jiaxin nodded sheepishly.

After studying at Princeton for several years, she learned not only computer science, but also a lot of mathematics. It's just that she has never shown much of her mathematical ability.

Especially after taking over Chuanhai Network Technology Co., Ltd., in order to build a security protection platform, there was very little time to study mathematics.

It wasn't until the protective platform came online last year that she devoted some of her time and energy to mathematics.

The NP=P problem was originally one of the mathematical directions she studied when she was a PhD student at Princeton. Now she has picked it up again, with the ultimate goal of studying artificial intelligence.