CHAPTER 687: CHAPTER 215: SITTING AND DISCUSSING THE DAO

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

Qiao Yu snapped his fingers, then casually picked up a pen.

He continued his enthusiastic introduction: "You can understand it as the latest extension of the Generalized Modal Axiomatic System, which I’ve named the Qiao Yu Modal Space. Its goal is to transcend the limitations of Hilbert space while still maintaining a consistent mathematical framework."

Peter Schultz frowned and asked, "But in quantum mechanics, the descriptions of superposition states and entangled states rely heavily on the framework of Linear Algebra. How do you circumvent this?"

Qiao Yu casually drew a curve on the manuscript, then showed it to Peter Schultz.

"Do you see this curve? It’s a simple modal path in the space, but I treat it as a mapping relation from the quantum initial state to the end state, rather than a set of superposed base states.

Every point on this path can describe the probability distribution of the quantum state through a modal density function, and the overall topological characteristics of the manifold will naturally integrate the effects of superposition and entanglement."

Peter Schultz glanced at Qiao Yu, while his brain was racing with thoughts.

He was shocked by Qiao Yu’s ambition, while also contemplating the feasibility of this idea.

Despite Qiao Yu’s simplification, it was obvious that there were many challenges to achieve this.

The simplest question is whether the modal path can strictly correspond to the mapping of the quantum state’s physical evolution?

The so-called Quantum Uncertainty Principle, when reflected in the mathematical curve describing the quantum state, represents high dimensionality.

After all, the explanations of dimensions in mathematics and physics are entirely different. Physically, one-dimensional, two-dimensional, and three-dimensional refer to spatial changes, but mathematically, high dimensionality represents the parameter space or the dimension of variables.

Simply put, mathematical dimensions are about the increase in various variables.

Describing a quantum system requires introducing more degrees of freedom.

A system requires multiple independent variables, including position, momentum, energy, velocity, etc. These variables jointly define a high-dimensional state space. This space is entirely unrelated to physical space.

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

Just a simple thought made Peter Schultz realize that this system surely had a ton of issues to solve. No wonder this guy kept saying he was very busy, with absolutely no time to pay attention to him.

So Peter Schultz shrugged and said, "Qiao Yu, I roughly understand your idea! I admit, your thinking is very advanced. Indeed, it is very meaningful! But this is not work that can be completed in a short time.

Of course, I’m not saying you have to devote all your energy to our collaboration. But you should allocate your time reasonably. Well, perhaps we can even collaborate bilaterally.

Maybe in a few years, the projects we’ve been striving for could yield results concurrently. Your Qiao Yu Modal Quantum Space, and my Condensed State Mathematics, wouldn’t you agree?"

After listening to this complaint, Qiao Yu looked puzzled at Peter Schultz and said, "Peter, you said a few years? Are you kidding? Building a spatial system to study quantum mechanics still needs several years? Is your time so worthless?"

Peter Schultz looked at Qiao Yu in amazement, unable to react for a moment.

This idea shouldn’t take several years for results; could it really take just a few months?

"What do you mean?" Peter Schultz asked.

"I’ve been busy recently because I want to perfect my Qiao Yu Modal Space for the report on the sixteenth."

Qiao Yu said seriously.

Peter Schultz instinctively swallowed, looking at Qiao Yu as though he wasn’t joking.

So he frowned, pointed at the curve Qiao Yu had casually sketched earlier, and asked, "First, about this curve, you mentioned treating it as a mapping relation from the quantum initial state to the end state.

It also includes Quantum Superposition Entangled States. How do you achieve this? Or, since the essence of the Uncertainty Principle lies in the probability distribution characteristics of quantum states, how do you embed these into the curve description?

If you plan to construct this space very quickly, this problem should already have an answer, right?"

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

After saying that, he started fiddling with the computer.

Though just an office, it was fully equipped with modern facilities, including a small projector.

Soon, the screen opposite slowly descended, and Qiao Yu directly projected the relevant content from his document onto the large screen via the computer.

Peter Schultz turned to look at the screen content and his brain began to work overdrive.

Hmm, using the modal density function ρM(p) to model, representing the probability distribution caused by the uncertainty in quantum states.

This way, each point p on the modal path has a function to describe the probability. Then, use a weighting function to define the correlation intensity between different points...

However, these still need calculations, and he currently doesn’t have the conditions for it. He can only silently verify them in his mind.

After watching for more than ten minutes, Peter Schultz finally spoke: "How do you distinguish between the superposition and entanglement when the path forks?"

Qiao Yu quickly pulled out another part of the argument content.

This time, Peter Schultz watched even longer.