Chapter 217 Sit and talk
Peter Schultz looked at Qiao Yu, who was so energetic, without saying a word.
After snapping your fingers, Qiao Yu picked up a pen casually.
I was still introducing attentively: "You can understand it as the latest extension of the generalized modal axiom system, and I named it Qiao Yu modal space. Its goal is to transcend the limitations of Hilbert's space. , while still maintaining a self-consistent framework in mathematics. "
Peter Schultz asked with a frown: "But in quantum mechanics, the description of superimposed states and entangled states relies heavily on the framework of linear algebra . How do you get around this? ”
Qiao Yu casually drew a curve on the manuscript and showed it to Peter Schultz.
"See this curve? This is a simple modal path in space, but I treat it as a mapping relationship from the initial quantum state to the final state, rather than a group of superpositions Ground state.
Each point in this path can describe the probability distribution of quantum states through a modal density function, and the overall topological characteristics of the manifold will naturally integrate into the effects of superposition and entanglement."< br>
Peter Schultz glanced at Qiao Yu, and his brain was thinking quickly.
He was shocked by Qiao Yu's ambitions. At the same time, I was also thinking about the feasibility of this idea.
Although Qiao Yu said it simple, it is obvious that there are many problems to do this.
The simplest thing is, can the mapping of modal paths and quantum state physical evolution strictly correspond?
The so-called principle of quantum uncertainty, reflected in the mathematical curve describing quantum states, represents a high dimension.
After all, mathematics and physics explain dimensions completely differently. Physically, one-dimensional, two-dimensional, and three-dimensional refer to changes in space, but mathematically, high-dimensionality represents the parameter space of a function or the dimensions of a variable.
Simply put, the mathematical dimension is the increase of various variables.
To describe a quantum system, more degrees of freedom must be introduced.
A system requires multiple independent variables, including position, momentum, energy, velocity, etc. These variables jointly define a high-dimensional state space. This space has nothing to do with physical space.
Although high dimensions of physics can be converted into mathematical variable dimensions through appropriate mapping relationships, and high-dimensional topology can describe the complexity of quantum states, specific mapping methods need to be pointed out.
Just think about it simply, Peter Schultz knew that this system must have tons of problems that need to be solved. No wonder this guy kept saying he was very busy and had no time to pay attention to him.
So Peter Schultz spread his hands and said, "Qiao Yu, I probably understand your idea! I admit that your idea is very advanced. It is indeed very meaningful! But this is not a short-term Work that can be done.
What I mean certainly is not that you have to focus all your energy on our cooperation. But you should allocate your time reasonably. OK, maybe we can work together in both directions.
In this way, maybe in a few years, the projects we work hard for will achieve results at the same time. Do you think your Qiao Yu modal quantum space, my condensed state mathematics, right? "
After hearing this person's complaint, Qiao Yu looked at Peter Schultz in confusion and said, "Peter, how many years did you say? What a joke? How many years will it take to build a space system that studies quantum mechanics? Is your time so worthless? "
Peter Schultz looked at Qiao Yu in surprise, but he didn't react for a while.
This idea will not take several years to achieve results. Is it enough for a few months? >
"What does it mean?" Peter Schultz asked. "I'm busy lately because I want to improve my Qiao Yu modal space when I was giving a report on the 16th." Qiao Yu said seriously.
Peter Schultz subconsciously swallowed his saliva, and Qiao Yu didn't seem to be joking.
So frowned, pointed to the curve that Qiao Yu had just drawn, and asked, "Talk about this curve first, you just said that you regarded it as a mapping from the initial state of quantum to the final state of the quantum Relationship.
It also includes quantum superposition entangled states. So how did you do this. In other words, the principle of uncertainty is essentially the probability distribution characteristics of quantum states. How did you embed these into the curve description?
If you want to build this space in a very short time, this question should have an answer, right? "
Qiao Yu nodded and said, "You can wait." ”
After saying that, he began to fiddle with the computer.
Although it was just an office, it had all kinds of modern facilities, including a small projector.
Soon the curtain opposite slowly fell, and Qiao Yu also projected this part of the content in his document on the computer directly onto the big screen.
Peter Schultz turned his head to look at the content on the curtain, and his brain began to run overload.
Well, the probability distribution caused by uncertainty in quantum states is represented by modeling the modal density function ρM(p).
In this way, each point p on the modal path has a function to describe the probability. Then, through the weight function, the correlation intensity between different points is defined...
However, these still require calculations, and he does not have this condition at present. It can only be verified silently in the heart by the brain.
After watching this for more than ten minutes, he spoke, "How to distinguish between the superposition and entanglement of path forks?"
Qiao Yu quickly brought up another part of the argument.
This time, Peter Schultz watched it longer.
"Okay, let's first assume that the modal path you designed can accurately describe the evolution of a single quantum state in this space. But a quantum field is composed of no quantum states. How can a single modal path be generalized to the field theory state distribution? ”
“I considered two methods for this question, and finally chose the method of spatial superposition. Directly construct a high-dimensional superposition structure.”
...
All the morning passed by inquiry and show. At twelve o'clock, Peter Schultz didn't know whether he was hungry or not, but he was really hungry.
There is no way, young people are completely inferior to these old men when fighting hunger.
So, while talking about a technical point, Peter Schultz continued to ask questions, he suggested, "It's better to go to have a meal first after twelve o'clock."
" Ah? Is it already twelve o'clock? So soon?" Peter Schultz, who came to his senses, was a little surprised and asked in a daze.
Qiao Yu nodded and pointed to the clock hanging behind him.
Peter Schultz glanced at it and it was indeed five minutes past twelve. "Someone asked me to have a meal at noon." Peter Schultz suddenly thought of this and took out his cell phone. Sure enough, there were several missed calls.
When I came here, I thought I would only talk to Qiao Yu about the few problems he encountered in recent research, and by the way, I would like to mention Qiao Yu. Thinking that it would take too much time, I mute my phone.
Stop disturbing the two people's discussion. Who would have thought that Qiao Yu would lead the class to the nose, and then obviously, he completely forgot about time.
"Forget it, I'll still not go when I call back. Maybe we can have dinner together at noon. I still have some questions about your Qiaoyu modal quantum space."
"It's Qiao Yu's modal space. In fact, it can not only describe quantum states, but also has many other uses at other levels."
Jo Yu corrected Peter Schultz's statement.
Peter Schultz shrugged, and did not express his opinion on Qiao Yu's rigor. He stood up and went to find a place to call back, while Qiao Yu found the student card from his bag.
Of course, I went to the nearby A Station to invite guests to dinner. Not only are they very close, but they are also of high quality, and they can also swipe cards. The most important thing is that now, Mr. Yuan doesn’t need to support him, he can also scan his face.
Then Qiao Yu found out that he had made a mistake.
Although he can indeed scan his face, the Institute A is particularly lively today.
Especially when the two young Fields Medal winners arrived together, they attracted a lot of attention without surprise.
In this case, it is almost impossible to be completely quiet and not disturbed. There will always be someone who will come and chat with you.
No mistakes, one song, one content, one in 6, one book, one bar, one reading!
Fortunately, everyone is highly educated. I saw that the two of them had something to say, and they both chatted and left with a few words.
Even so, the two of them couldn't communicate as well as they were in the office. Not everyone can get used to thinking being interrupted.
But, although Qiao Yu did not say it clearly during this meal, Peter Schultz still keenly understood Qiao Yu's current troubles and developed a strong interest.
It was natural that Peter Schultz was forced to control himself, and then turned down everything in the afternoon, and followed Qiao Yu back to Qiuzhai honestly.
Mr. Yuan was also there in the afternoon. Qiao Yu took Peter Schultz to Mr. Yuan’s office first and greeted him, and then returned to his office under the urging of Peter Schultz.
Peter Schultz couldn't wait to give his own judgment after thinking.
"Your idea is good, but the problem of local-global unity is difficult to solve. After rising to the global, it is impossible for ultra-high-dimensional structures to ensure the uniqueness of modal paths every time they are mapped. ! ”
Jo Yu looked at Peter Schultz with appreciation. To be honest, this gaze made Peter Schultz not very adaptable.
No one has looked at him with this kind of gaze for a long time. The last time someone looked at him with this kind of eyes was when he graduated from a doctorate.
As for Qiao Yu, he obviously did not suffer from these problems. He just felt that it was easy to discuss such academic issues with smart people online. Just need a little guidance to quickly grasp the key points.
This is much more comfortable than talking to those guys in the computing institute, and they often talk to each other.
But that wasn't what Qiao Yu said when he opened his mouth.
"This is indeed a problem, but I already have a solution, and there is more than one. Actually, this problem is not very difficult.
You can use topological constraints of modal paths to reduce the possibility of paths, or to correct the consistency of the introduced paths every time. Both methods can solve this problem."
As he said that, Qiao Yu pulled out the solution he had thought about before.
Although he was not satisfied with these two solutions, he must not be weak in momentum.
Peter Schultz can't think he can't handle this problem for the time being, so he really wants to talk to him to see if he can have any inspiration.
Sorry, before getting this problem solved, these foreigners can't taste a little sweetness, even spiritual pleasure.
After all, for a mathematician like Peter Schultz who is no longer short of money, spiritual gains are often happier than material gains.
Peter Schultz began to think again. Qiao Yu picked up the water that he put at hand and began to think.
There is no way to solve this problem.
After a long time, I don’t know how long it was quiet in the office, Peter Schultz frowned and said, “The combination of these two methods is too much calculation! I don’t think it’s very suitable.”
Peter Schultz's voice interrupted Qiao Yu's thoughts.
Qiao Yu quickly passed the meaning of Peter Schultz in his mind, and then said with confidence: "Actually, I have thought about your ideas carefully.
It's from the high A rule is found in the properties of the dimension map itself, which makes the branches of the modal path statistically controllable. "
Peter Schultz thought for a while and asked, "You mean from the probability Introduce the optimal path selection mechanism from the angle? For example, constructing a path weight function to unify the path and distribution probability globally? "
"That's right!" Qiao Yu nodded with certainty, and then began to learn from one example and apply it to other things. .
"The key is to let the system choose the optimal path itself, rather than imposing constraints artificially. This must be determined from the basic weight construction rules. My previous plan was to use the path stability indicator as the initial condition. ”
He never thought that this was what Qiao Yu had just thought of. To judge others by oneself, at least his thinking is not so fast.
In fact, Peter Schultz is still marveling at the efficiency of Qiao Yu in his research.
He couldn't understand how Qiao Yu did it at all. It is not new to mathematicians occasionally have a flash of inspiration and then solve a global problem. But you can't keep flashing, right?
Can people have no bottlenecks? You should know that Qiao Yu just solved the Riemann conjecture not long ago.
When everyone thought he would continue to work on the number theory, he created a modal space for Qiao Yu...
Peter Schultz considered himself a genius, but in fact, most people in the world are Think so.
But today Qiao Yu taught him a lesson, which made him feel that life was quite boring.
It is no exaggeration to say that his condensed matter math project is too lazy to continue. I always feel that the future uses are not as useful as Qiao Yu's generalized modal axiom system.
It is no exaggeration to say that if Qiao Yu's system continues to expand like this, it can completely replace his condensed matter mathematics.
After all, his ultimate goal is to provide simpler tools and verify complex theorems in studying such as algebraic geometry, algebraic topology and high-dimensional category theory.
It is obvious that his ultimate goal, Qiao Yu's generalized modal axiom system, can he do that, why does he have to do that?
(This chapter ends)