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Chapter 217 Sitting and talking

Peter Schultz looked at the high-spirited Qiao Yu without saying a word.

Qiao Yu snapped his fingers and picked up a pen.

He continued to introduce diligently: "You can understand it as the latest extension of the generalized modal axiom system. I named it Qiao Yu modal space. Its goal is to transcend the limitations of Hilbert space while maintaining a mathematically self-consistent framework."

Peter Schultz frowned and asked, "But in quantum mechanics, the description of superposition and entanglement depends 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? It’s a simple modal path in space, but I think of it as a mapping from the initial quantum state to the final quantum state, rather than a set of superpositions of ground states.

At each point on this path, the probability distribution of the quantum state can be described by a modal density function, and the overall topological properties of the manifold naturally incorporate the effects of superposition and entanglement.”

Peter Schultz glanced at Qiao Yu, his brain thinking rapidly.

He was shocked by Qiao Yu's ambition, and at the same time he was thinking about the feasibility of this idea.

Although what Qiao Yu said was simple, it is obvious that there are many problems in achieving this.

The simplest thing is, can the mapping between the modal path and the physical evolution of the quantum state strictly correspond?

The so-called quantum uncertainty principle, reflected in the mathematical curves that describe quantum states, represents higher dimensions.

After all, mathematics and physics have completely different interpretations of dimensions. In physics, one, two, and three dimensions refer to changes in space, but in mathematics, high dimensions represent the parameter space of a function or the dimension of a variable.

Simply put, 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., which together define a high-dimensional state space. This space has nothing to do with the physical space.

Although physical high dimensions can be converted into mathematical variable dimensions through appropriate mapping relationships, and high-dimensional topological structures can describe the complexity of quantum states, the specific mapping method needs to be pointed out.

Just by thinking about it, Peter Schultz knew that this system must have tons of problems to solve. No wonder this guy kept saying that he was busy and had no time to pay attention to him.

So Peter Schultz spread his hands and said, "Qiao Yu, I roughly understand your idea! I admit that your idea is very advanced and indeed very meaningful! But this is not a task that can be completed in a short period of time.

I certainly don't mean that you have to focus all your energy on our cooperation. But you should allocate your time reasonably. Well, maybe we can still cooperate in both directions.

In this way, maybe in a few years, the projects we are working on will be able to produce results at the same time. Your Qiaoyu modal quantum space and my condensed matter mathematics, do you think it is right?"

After listening to this person's complaint, Qiao Yu looked at Peter Schultz in confusion and said, "Peter, what years are you talking about? Are you kidding me? How many years does it take to build a space system to study quantum mechanics? Is your time so worthless?"

Peter Schultz looked at Qiao Yu in astonishment and didn't react for a moment.

This idea will take several years to bear fruit, so will a few months be enough?
"What do you mean?" Peter Schultz asked.

"I've been busy lately because I want to perfect my Qiao Yu modal space for my report on the 16th."

Qiao Yu said seriously.

Peter Schultz swallowed subconsciously and saw that Qiao Yu didn't seem to be joking.

So he frowned, pointed at the curve that Qiao Yu had just drawn, and asked, "Let's talk about this curve first. You just said that you can regard it as a mapping relationship from the initial quantum state to the final quantum state.

It also includes quantum superposition and entanglement. So how do you do this? In other words, the uncertainty principle is essentially the probability distribution characteristics of quantum states. How do you embed these into the curve description?

If you want to build this space in a short time, this question should already be answered, right? "

Qiao Yu nodded and said, "Wait a moment."

After saying that, he started fiddling with the computer.

Although it is just an office, it is equipped with all modern facilities, including a small projector.

Soon, the curtain on the opposite side slowly fell down, and Qiao Yu projected the contents of his document on the computer directly onto the big screen.

Peter Schultz turned his head to look at what was on the screen, and his brain began to work in overload.

Well, it is modeled through the modal density function ρM(p) to represent the probability distribution caused by the uncertainty of the quantum state.

In this way, each point p on the modal path has a function to describe the probability. Then, the weight function is used to define the strength of the association between different points...

However, these still need to be calculated, and he currently does not have the conditions to do so. He can only rely on his brain to silently verify it in his mind.

After watching for more than ten minutes, he finally asked, "How do you distinguish between superposition and entanglement of bifurcated paths?"

Qiao Yu quickly brought up another part of the argument.

This time, Peter Schultz looked longer.

"Okay, let's 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 countless quantum states. How can a single modal path be extended to the state distribution in field theory?"

"I considered two methods to solve this problem, and finally chose the method of spatial superposition. Directly construct a high-dimensional superposition structure."

……

In this way, the whole morning passed with questions and demonstrations. At twelve o'clock, Qiao Yu didn't know whether Peter Schultz was hungry or not, but he was really hungry.

There's no way. Young people are no match for these old men when it comes to fighting hunger.

So after he finished talking about a technical point, before asking more questions, Peter Schultz suggested, "It's already past midnight, why don't you go eat first?"

"Ah? Is it twelve o'clock already? So soon?" Peter Schultz, who had come 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 looked and saw that it was already five minutes past twelve.

"Someone asked me out for lunch at noon." Peter Schultz suddenly thought of this, then took out his cell phone, and sure enough, he had several missed calls.

When I came here, I had intended to just chat with Qiao Yu about a few problems he had encountered in his recent research, and give Qiao Yu some advice. Thinking it wouldn't take long, I turned my phone to silent mode.

So as not to disturb the discussion between the two. Who would have thought that Qiao Yu would lead him to class as soon as he arrived, and then it was obvious that he had completely forgotten the time.

"Forget it, I'll call you back later. I'm not going. Maybe we can have lunch together at noon. I still have some questions about your Qiao Yu modal quantum space."

"It's a metaphor for modal space. In fact, it can do more than just describe quantum states. It has many other uses at other levels."

Qiao Yu corrected Peter Schultz's statement.

Peter Schultz shrugged his shoulders and did not comment on Qiao Yu's rigor. He stood up and went to find a place to answer the phone. Qiao Yu took out his student card from his bag.

When inviting people to dinner, he naturally went to the nearby Jiasuo. Not only was it very close, it was also of a higher grade and accepted credit cards. Most importantly, he no longer needed Mr. Yuan to back him up, he could also use facial recognition.

Then Qiao Yu realized that he had made a mistake.

Although he can indeed use his face to get things done, Office A is particularly busy today.

Especially when two still very young Fields Medal winners came together, it unsurprisingly attracted a lot of attention.

People cannot live without society, so it is almost impossible to be completely quiet and undisturbed in this situation. There will always be someone to come and chat with.

Fortunately, everyone had received higher education, and when they saw that the two had something to say, they all chatted politely for a few words and then left.

Even so, the two of them couldn't communicate as smoothly as they did in the office. Not everyone is used to having their thoughts interrupted.

But during this meal, although Qiao Yu did not say it explicitly, Peter Schultz was still keenly aware of Qiao Yu's current troubles and became very interested.

Naturally, Peter Schultz was controlled and put aside all his afternoon tasks, and obediently followed Qiao Yu back to Qiuzhai.

Mr. Yuan was also there in the afternoon. Qiao Yu took Peter Schultz to Mr. Yuan's office to say hello, and then, at Peter Schultz's urging, returned to his own office.

Peter Schultz couldn't wait to give his own judgment after thinking it over.

"Your idea is good, but the problem of local-global unity is difficult to solve. After rising to the global level, it is impossible for the ultra-high-dimensional structure to guarantee the uniqueness of the modal path every time it is mapped!"

Qiao Yu looked at Peter Schultz with admiration. To be honest, Peter Schultz was not used to this look.

It had been a long time since anyone looked at him like this. The last time someone looked at him like this was when he graduated with his doctorate.

As for Qiao Yu, he was obviously not bothered by these things. He just felt that it was easy to discuss such academic issues with smart people whose brains were online. He only needed a little guidance to quickly grasp the key points.

This is much more comfortable than discussing problems with those guys in the Institute of Computing Technology, where we often have different opinions.

But Qiao Yu didn't say that when he opened his mouth.

"This is indeed a problem, but I have already found a solution, and there is more than one solution. In fact, this problem is not very difficult.

This problem can be solved by either using topological constraints on the modal paths to reduce the number of possible paths or by performing consistency checks on the incoming paths each time. ”

As he spoke, Qiao Yu casually brought out the solution he had thought of before.

Although he was not satisfied with either of these two solutions, he absolutely could not weaken in momentum.

I can't let Peter Schultz think that he can't solve this problem for the time being, so I really want to talk to him and see if he can give me any inspiration.

I'm sorry that before this problem is solved, these foreigners cannot enjoy even the slightest bit of sweetness, even spiritual pleasure.

After all, for a mathematician like Peter Schultz who is no longer short of money, spiritual gains are often more enjoyable than material gains.

Peter Schultz began to think again. Qiao Yu picked up the water beside him and began to think as well.

There is no way this problem is difficult to solve.

After a long while, and I don’t know how long the office was silent, Peter Schultz frowned and said, “The combination of these two methods requires too much calculation! I don’t think it’s suitable.”

Qiao Yu immediately retorted: "But it can be simulated accurately."

"No, no, no. The uncertainty principle dictates that the quantum world doesn't need to be that precise. I personally think you should use this uncertainty instead of always thinking about how to eliminate it."

Peter Schultz's voice interrupted Qiao Yu's thoughts.

Qiao Yu quickly went over Peter Schultz's meaning in his mind, and then said confidently: "In fact, I have also thought carefully about your idea.

It is to find a law from the properties of the high-dimensional mapping itself, so that the branching of the modal path is statistically controllable. "

Peter Schultz thought for a moment and asked, "Do you mean to introduce an optimal path selection mechanism from a probability perspective? For example, construct a path weight function to globally unify the path and distribution probability?"

"That's right!" Qiao Yu nodded affirmatively, and then began to draw inferences from his example.

"The key is to let the system choose the optimal path itself, rather than impose constraints manually. This needs to be determined from the basic weight construction rules. My previous plan was to use the path stability index as the initial condition."

He didn't think that this was what Qiao Yu had just thought of. Judging from his own experience, at least his thinking was not so fast.

In fact, Peter Schultz is still amazed at Qiao Yu's efficiency in academic research.

He couldn't understand how Qiao Yu did it. It was not uncommon for mathematicians to have a flash of inspiration occasionally and then solve a world-wide problem. But it's impossible for the flashes of inspiration to continue, right?

Can a person be free of bottlenecks? You know, Qiao Yu just solved the Riemann hypothesis not long ago.

When everyone thought he would continue to delve deeper into number theory, he came up with a metaphorical modal space...

Peter Schultz also considers himself a genius, and in fact most of the world thinks so.

But today Qiao Yu taught him a solid lesson, which made him feel that life was rather boring.

It is no exaggeration to say that I am too lazy to continue his condensed matter mathematics project. I always feel that it will be less useful in the future than Qiao Yu's generalized modal axiom system.

It is no exaggeration to say that if Qiao Yu's system continues to expand in this way, it can completely replace his condensed matter mathematics.

After all, his ultimate goal is to provide simpler tools and verify complex theorems in the study of algebraic geometry, algebraic topology and high-dimensional category theory.

It is obvious that his ultimate goal can be achieved by Qiao Yu's generalized modal axiom system, so why should he bother with that?
(End of this chapter)