Chapter 217 XuWeylBerry Theorem and High Dimensional Space

Time passed quickly, forty-five minutes passed in the blink of an eye.

On the podium, Xu Chuan began to finish the explanation of this report meeting.

"In summary, all the methods mentioned above, using the Xu-Weyl-Berry theorem for split twisting, can use different eigenvalues, boundary values, optical boundary information and other data to calculate the complete source parameters."

Xu Chuan's voice reached the ears of everyone in the conference venue clearly and surely.

The sound is not loud, but it seems like the voice of truth surrounds the ears, making people intoxicated.

And that source is knowledge and wisdom.

"This is an expanded application of the Xu-Weyl-Berry theorem."

When the last sentence came out, some of the scholars in the audience suddenly stood up and applauded from their hands.

Immediately, others quickly stood up, and thunderous applause resounded in an instant, lasting for a long time in this wide and crowded venue.

This is a lesson, a lesson of truth woven with knowledge and wisdom.

And they are all students.

On the stage, Xu Chuan finished explaining the extended application of the Xu-Weyl-Berry theorem and looked at the audience with a smile.

After scanning around the people in the venue, his eyes fell on a figure in the front row.

Sal Perlmutter stood there, smiling and looking at Xu Chuan, his eyes conveying approval.

Xu Chuan smiled and nodded, looking towards the venue.

"The first half of the report on the expanded application of the Xu-Weyl-Berry theorem has been completed. The following will be time for questions. If you have any questions, please feel free to ask them. If I know, I will answer it."

As soon as he finished speaking, someone in the venue raised their hands.

Xu Chuan nodded, and the person who raised his hand stood up again and asked: "Professor Xu, in the application context, each eigenvalue λi can be regarded as making some kind of measurement of Ω, so figuratively speaking, The above isospectral problem means that if the data obtained for Ω1 and Ω2 under all those (infinitely many) measurements are the same, can it be geometrically deduced that Ω1 and Ω2 can completely overlap? "

Xu Chuan nodded and said: "Before the Xu-Weyl-Berry theorem appeared, the answer we got was generally negative.

"However, there are counterexamples. For example, Milnor constructed a pair of 16-dimensional torus that are isospectral but not isometry. Research in this area involves analysis (spectrum of elliptic operators), geometry, topology and other disciplines. Crossover content.”

"Of course, now using the Xu-Weyl-Berry theorem, it can be derived geometrically at the same time. It is part of the Xu-Weyl-Berry theorem."

"Thank you." The person who raised his hand to ask thanked him and sat down with some contemplation in his eyes.

On the podium, Xu Chuan continued to host the report meeting and then answered some questions from others.

He spent forty-five minutes explaining the one-hour report, and the remaining fifteen minutes for questions were not long and passed in the blink of an eye.

As the end came to an end, Xu Chuan also breathed a sigh of relief and prepared to end the report meeting.

Suddenly, someone in the audience raised his right hand.

Xu Chuan looked over and was a little surprised. The person who raised his hand was Professor Brian Schmidt, who had led the standing ovation before. Like Sal Perlmutter, he was also the 2011 Nobel Prize winner in physics.

He was still a little curious about a Nobel Prize winner raising his hand, not knowing what the other person wanted to ask.

After the signal passed, Professor Brian Schmidt stood up and asked: "Professor Xu Chuan, regarding the expanded application of the Xu-Weyl-Berry theorem, can it be further extended to high-latitude space?"

Hearing this, Xu Chuan frowned slightly, thought for a while and then asked: "I wonder what the high-latitude space you are talking about refers to?"

"High latitude in physics!" Professor Brian Schmidt said calmly.

Hearing this, the entire venue was silent for a moment, and then there was an uproar.

Everyone started discussing, and the questions raised by Professor Brian were really amazing.

In a corner of the venue, among the NTU team, Chen Zhengping couldn't help but sigh: "This idea is really crazy."

At NTU, he was the first to understand Professor Brian’s idea, which I have to say is really crazy and whimsical.

On the side, Cai Peng, a student of Professor Zhou Hai, asked curiously: "Professor, what does it mean to calculate high latitude? Isn't the expanded application of the Xu-Weyl-Berry theorem itself a method of calculating information points?"

He still has some research on the Xu-Weyl-Berry theorem.

During his graduate studies, his main focus was on boundary values ​​and fractal drums, but he later changed his research field.

He has read both Xu Chuan's weak Weyl-Berry conjecture and the proof papers of the Weyl-Berry conjecture, and has some understandings of his own.

I thought I had a deep enough understanding of the Xu-Weyl-Berry theorem, but when I came to listen to the report today, I found that I still fell far behind. Many of the things that I had not cleared up before, or were hazy, now have ideas.

However, he still couldn't keep up with the opponent's rhythm.

In addition, I have basically no physical ability. Although I have some ideas about the ideas proposed by Professor Brian, I cannot fully understand them.

Moreover, to be honest, he couldn't believe it.

As Chen Zhengping said, this is too crazy and shocking.

On the side, Zhou Hai smiled and said, "Don't you already have an idea in your mind?"

Hearing this, Cai Peng couldn't help but swallow.

It would be amazing if this could really be done.

In mathematics and physics, high latitude is not the same concept.

In mathematics (Euclidean geometry), dimensions are used to describe the position of a point.

All dimensions are equal like other dimensions. The 4th dimension is like a hypercube. Pure geometric concepts have no concept of time.

In science fiction, more mentions are made of time travel. Traveling from low dimensions to high dimensions may also come from geometric concepts.

But in fact, there is no such concept in mathematics.

However, it is different in physics, and there are different types in high-dimensional physics.

For example, in classical mechanics, time is not the fourth spatial dimension. Time is used to describe the way physical changes occur.

Or, for example, in the special theory of relativity of Poincaré and Einstein, time is treated as a separate dimension.

The earth we live in today is a three-dimensional world with length, width and height. If the dimension of time is added to this three-dimensional world, it becomes four-dimensional.

The passage of time in the universe is a four-dimensional space. If we can locate and calculate the dimension of time, we may be able to travel through the past and the future.

Of course, no one knows whether it can be done.

But what is certain is that this question raised by Professor Brian Schmidt instantly detonated the whole audience again.

Everyone is talking.

If the extended application of the Xu-Weyl-Berry theorem can be used to calculate high-latitude spaces, it may bring drastic changes to mankind.

Einstein's theory of relativity will once again be confirmed, and high-latitude space does exist.

Can humans find a way to explore and enter the high-latitude world?

If the fourth dimension is really time, is there a way to reverse time and create time machines like those in science fiction movies and novels?

Everyone is talking, but no one can give an answer.

If there is an answer, I'm afraid only the young man on the stage can know it.

Thinking and discussing, everyone in the venue turned their attention to the podium again.

On the podium, Xu Chuan was also deep in thought.

It has to be said that Professor Brian Schmidt raised questions that he had never thought of before.

Mathematical dimensions and physical dimensions are not the same concept. No matter how high the mathematical dimension is, it is just something created to describe a marked point.

But the physical dimension is completely different.

But, what should be done to use the extended application of Xu-Weyl-Berry theorem to calculate high-latitude space?

The fourth dimension, is it really time?

The theory recognized by the modern physics community and founded by German physicist Bachhard Heim in 1957 is eight-dimensional space.

Divided into X dimension (length of object), Y dimension (width of object), Z dimension (height of object), time dimension, gravity dimension, electromagnetic force dimension, universal gravitation dimension, and universal repulsion dimension.

This is relatively close to the multi-dimensional space we know today, and it can also be confirmed by experiments.

Later, his mentor Edward Witten unified string theory, which proposed some unverifiable spaces, but its limitations were obvious and could not be verified.

Even in later generations, when he discovered things like gravitons, dark matter, and dark energy, he never studied high-latitude space.

Because this is too far away from him, so far away that even in another thousand years, humans will not be able to access this aspect.

For a moment, Xu Chuan felt like his head was going to explode.

After coming back from his thoughts, he shook his head, took a long breath, and said again: "I'm sorry, I can't give an answer to this question."

"However, at present, the extended application of the Xu-Weyl-Berry theorem does not have this ability. We cannot understand space and time, and we do not know whether four-dimensional space or higher-dimensional space really exists."

"Today, we know too little about the high-latitude world or high-latitude space. Even for speculation, there are only a few theories. Without information, it cannot be used as parameters such as boundary values ​​and eigenvalues, let alone No information about the fourth dimension can be found.”

Professor Brian Schmidt sighed and said, "Thank you."

After the mathematical tool of extended application of the Xu-Weyl-Berry theorem appeared, he was inspired to think of this aspect.

But it is a pity that he has not fully mastered this tool, and has not been able to go further on it, nor can he explore whether this tool can be used to calculate high-dimensional spaces, so he has put his hope to today.

pity

The one-hour report meeting ended, and the scholars in the venue gradually dispersed, but the commotion outside had just begun.

The news was transmitted very quickly, and within a short time, today's report had already spread throughout the entire mathematics, astronomy, and astrophysics circles, and it had a vague meaning of breaking the circle.

[Today’s report meeting was really exciting! 】

[What does Professor Brian Schmidt’s last question mean? I'm a little confused. Calculation of high-dimensional space? 】

[The Xu-Weyl-Berry theorem may be used to calculate whether four-dimensional space really exists. 】

[The kind of four-dimensional space in science fiction movies? 】

[Well, if you can calculate the high-dimensional space composed of length, width, height + time, you may be able to enter it, and you may be able to travel to the past and future. 】

【Oh My God! 】

【impossible? Can math calculate this? 】

[It is certain that mathematics can do it. All theories can be expressed in mathematics, but it should not be possible now. 】

[Hiss~, this is too scary. If you can travel to the past or the future, wouldn't this be a time machine? 】

Various discussions continued at the academic forum, not to mention that Xu Chuan, who was still at the International Congress of Mathematicians, was once surrounded by various scholars and reporters who knew the news.

Mathematical tools for calculating high-dimensional space, mathematics for opening four-dimensional space, and time machines, all of these things concern everyone's hearts.

"Can your method really not be used to calculate information in high-latitude space?" In the hotel, Chen Zhengping looked at Xu Chuan and asked, and he was also looking forward to it.

Xu Chuan shook his head and frowned: "Any calculation is based on obtaining data. We can't even obtain data now, how can we calculate it?"

"The Xu-Weyl-Berry theorem can calculate the parameter information of distant celestial bodies because various astronomical equipment actually observes various parameters of those celestial bodies. The mathematical method is just a further recalculation and optimization of those parameters. "

"As for high dimensions, we know too little. Those theoretical methods are always just theories, and there is no reliable real data. Except that we can feel the flow of time, we cannot obtain any other information."

"That's not how math works."

Xu Chuan shook his head and replied. At first, he was also shocked by Professor Brian Schmidt's question.

But after thinking about it carefully, I realized that this was something impossible to do.

At least not for the time being.

"Forget it, let's not talk about this anymore. We don't understand this thing. If there is any hope, it will either be with you or I don't know how many years in the future."

Chen Zhengping shook his head and continued: "How long do you plan to stay in Princeton? When do you plan to return to China?"

Xu Chuan smiled and said: "Come on, I will go back after this International Congress of Mathematicians is over."

He has never revealed to others his thoughts and time of returning to China, but it doesn't matter now.

After this International Mathematics Conference, he no longer plans to return to Princeton. He plans to fly directly from Brazil to Europe and then transfer back to China.

This is safer.

As for the materials and things in Princeton, you can just have them mailed back or brought back. If they are intercepted, then don’t do it.

Chen Zhengping was a little surprised and asked: "So fast?"

He originally thought that Xu Chuan would stay at Princeton for another year or two. After all, he was working with Fefferman to study the NS equation and had made preliminary results. There was great hope that he could solve the problem of the NS equation in the future. question.

Xu Chuan nodded and said with a smile: "No more delay, the higher-ups have already asked people from the organization bu to look for me."

Chen Zhengping suddenly realized and said with a smile: "Then do you want to come with us?"

Xu Chuan smiled and said, "Let's talk about it then. Things on my side haven't been arranged yet."