Chapter 578 Number Theory and the Mystery of Space and Time
After the opening ceremony, there were no report meetings scheduled in the afternoon.
Scholars who came to participate in the conference either left or looked for scholars and old friends they wanted to make friends with for communication.
In the evening, the banquet after the opening ceremony was held in the restaurant of Talon Imperial Hotel.
For this banquet, Talon Imperial Hotel not only prepared extremely sumptuous food, but also specially adjusted and changed the layout of the restaurant.
The original tables and chairs in the restaurant, especially those round tables that took up a lot of space, were dismantled and moved out of the restaurant by the hotel.
The purpose is to accommodate the thousands of scholars who come to attend the conference as much as possible.
As for the protagonists of the dinner, there is no doubt that they are the four, no, five scholars who have won the Fields Medal.
The Fields Medal is only awarded to scholars under the age of 40, and for the mathematics community, the age of 40 is the peak period of academic research.
For others, the scholars who receive awards each time are like stars, and just standing there can make others revolve around them.
Xu Chuan, who won the Fields Medal Special Award, was undoubtedly the core of the crowd. Almost every scholar who came to attend the lecture conference was squeezing this way, wanting to say hello to him.
"Congratulations, Xu, for winning another crown."
In the restaurant, Professor Fefferman gently clinked glasses with Xu Chuan while holding champagne, and congratulated him with a smile.
"Thanks."
Xu Chuan smiled and nodded, taking a sip of the champagne in the glass.
Fefferman smiled and said: "Speaking of which, you have solved the Yang-Mills existence and quality gap problems. What are you going to do next?"
After a slight pause, he added: "Leave aside the unified strong electricity theory."
Hearing this question, Xu Chuan smiled and shook his head and replied: "The future is too far away, and I can't be sure."
Fefferman raised his eyebrows and said with a smile: "There must be a direction. I don't believe that people like you don't have any plans for the future."
Hearing this, Xu Chuan thought for a moment and said, "Maybe you can study the Riemann Hypothesis or some of Einstein's theories?"
"I can understand the Riemann Hypothesis, but what are some of Einstein's theories...? I don't seem to have heard that you have studied this area of things?"
Fefferman looked at Xu Chuan curiously. If he could still understand the Riemann Hypothesis, he was, after all, a descendant of Grothendieck. Studying the Riemann Hypothesis and unifying algebra and geometry was almost the dream of this school of mathematicians, including him.
That old friend Deligne has also been studying this.
But I have never heard of Einstein’s theory being researched.
Of course, it is not ruled out that he suddenly wants to study it. After all, in addition to being a mathematician, he is also a physicist.
Xu Chuan smiled and said: "The main thing is Einstein's Rosen Bridge formula, which can help me understand the interaction of matter and energy in space and time, and can also combine the theory of relativity and quantum mechanics."
"You want to unify relativity and quantum mechanics?"
At this moment, another voice came from the side.
Xu Chuan and Fefferman looked up and saw that the speaker was Professor Faltings, a master in the field of algebraic geometry. Beside him, Deligne and Witten also walked over.
"Congratulations, you won the second Fields Medal in your life." Witten smiled and stepped forward to congratulate him, then reached out and patted his student on the shoulder.
Xu Chuan smiled and said: "Thank you, I am also surprised that the International Mathematical Union would make such a decision."
Faltins: "You haven't answered my question yet."
"Unifying the theory of relativity and quantum mechanics? That's too difficult. I'm just more interested in Einstein's Rosen Bridge." Xu Chuan glanced at the Germanic old man with curiosity, not quite understanding why he suddenly paid attention to this issue.
.
"You want to calculate the space void mathematically?" Faltings asked quickly.
"Yeah." Xu Chuan nodded and said with a smile: "Try it. If you can do it mathematically, you might have a chance to calculate some real bridges in physics."
Faltings thought for a moment and looked over with some interest. No wonder Schultz said he would be interested.
Faced with this problem, let alone him, I am afraid that most scholars in the world will be interested.
If the existence of Einstein Rosen Bridge can be confirmed, it will be an extremely shocking achievement for the academic community, no, for the entire world.
After thinking for a moment, he quickly asked: "What's the problem?"
Xu Chuan was stunned for a moment and looked at Faltings with some confusion.
Faltings: "You should have studied this problem, so what problems did you encounter in it?"
Xu Chuan shook his head and said: "There are too many problems. First, we have to find a real particle in the universe that can open or communicate with the Einstein-Rosen Bridge. Secondly, we may also need to determine or find the existence or several solutions to the gravitational field equation.
.Then bring in the material model, coordinate conditions and other information..."
"The series of troubles is just too much."
Hearing this, Faltings frowned slightly: "This is a bit of a mess, haven't you found the end?"
Just as Xu Chuan was about to answer, Witten on the side spoke: "There must be some threads. Although I don't know the progress of his research on Einstein's Rosen Bridge, he should have first assumed the existence of the particle that can open space and time.
Then make deductions based on this.”
After a pause, he continued: "The foundation of the Einstein Rosen Bridge is the gravitational field equation, and Riemannian geometry is used to describe the space-time background. If you want to solve this problem..."
After thinking for a while, Witten continued: "Maybe you can consider the correlation function and the analytic continuation on the complex plane before doing this job?"
Compared with Faltings, he has a deeper foundation in physics. String theory is the idea he used to unify relativity theory and quantum theory, so he saw through Xu Chuan's theoretical foundation at a glance, and even more importantly
A new idea is provided on this basis.
This chapter is not over, please click on the next page to continue reading! "Associated functions..."
Hearing this term, Xu Chuan touched his chin and started thinking.
If we say the most famous problem in the field of functions, it must be the Riemann Hypothesis.
So far, there are thousands of mathematical propositions based on the establishment of the Riemann Hypothesis and its generalized form. If the Riemann Hypothesis is confirmed, then all the formulas and conclusions calculated by mathematicians based on this conjecture for a long time will be
Confirm.
For the mathematical community, this is undoubtedly a magnitude 9 earthquake.
Not only that, if the Riemann Hypothesis is proven, many very important and cutting-edge advanced high-tech fields, such as finance, artificial intelligence, biological neural networks, and national security systems, will evolve accordingly.
It can be said that among the seven millennium problems, the Riemann Hypothesis is the most important one.
But he really didn’t think much about the expansion of the Riemann Hypothesis in the field of physics.
Because the Riemann Hypothesis belongs to an important branch of number theory in mathematics, and number theory has almost no applications in other disciplines.
However, Edward Witten's words gave him some inspiration and made him think of something else.
In the long period of studying the Riemann Hypothesis, countless mathematicians have made great contributions and achievements to this end.
One of the most famous ones is that 'the correlation function caused by the Riemann Hypothesis can actually correspond to the correlation function of the eigenvalues of the hermit matrix.'
The pair correlation function of the eigenvalues of a random Hermitian matrix is a function in physics that describes the energy level distribution of a multi-particle system under interaction.
A purely mathematical proof has found a corresponding map in the physical world. What does this mean?
This is a question Xu Chuan has never thought about before.
Now think about it, there is a huge amount of secret imagination contained in this.
Perhaps, in the pair correlation function of the eigenvalues of the random Hermitian matrix, he can find a functional formula to complete the distribution explanation of gravitons?
As for the space void existing in the universe, can the specific image be depicted by this distribution function?
If this is the case, he does not necessarily have to use topology and geometry to find and explore the mystery of Einstein's Rosen Bridge. Number theory is also possible.
How interesting.
On one side is the Riemann Hypothesis of pure mathematics, which is only about the purest mathematical properties such as the non-zero point distribution of a Zeta function. It reveals the elegant dance and rhythm of prime numbers in the sequence of natural numbers.
On the other side is the most realistic physical world, which connects quantum systems, disordered media, neural networks and other classical chaotic systems.
Unexpectedly, theory and reality would intersect here. After developing alone in a closed world for more than two thousand years, number theory, the most important branch of mathematics, might actually reach into the real realm of space and time.
...
PS: There is a bit of lag in the text. I am checking papers and information, and I am thinking about getting it out in a reasonable way. There is only one picture today. I will continue to code at night and see if I can post another one in the morning.
