Before this, we just used whatever tool was good and called it a day.
After seeing Yang Xuanqing shake his head, Edward Witten smiled and then said, "You see, that's exactly where the problem lies. It's not only his Quantum Implicative Model that he proposed; if you delve into Qiao Algebra and Qiao Geometry, you'll discover how wildly imaginative his thought process is. Those proof processes are so brilliant.
Do you know? This is the first time, even though he's written the papers, that I didn't grasp the deeper implications within. It wasn't until Qiao Ze told me that to understand those, it's not that complicated after all—just need to break away from the conventional mindset and use the Super Helical Coordinate System, and many problems will easily be solved."
Yang Xuanqing was somewhat bewildered and asked, "Double helix coordinate system?"
"Yes, the mathematical theoretical basis Qiao Ze used to design the Quantum Implicative Model," Edward Witten nodded and said.
Yang Xuanqing's expression was complex, as he suddenly felt that Qiao Ze was closer to these foreign professors after all; even he did not know about these theoretical things.
He had carefully looked over the twelve images Qiao Ze posted on Weibo; they did not concern this aspect. Or, to say they lacked complete mathematical derivation.
"Hmm... May I have a look?" Yang Xuanqing hesitated for a moment but still made the request, feeling slightly indignant inside. After all, Qiao Ze is a Huaxia person; shouldn't these things be popularized in the country first?
"Of course, you can even understand it more easily, because Professor Qiao really does as he pleases. The email he sent me about the derivations related to this was written in Chinese. In his words, if some concepts can't be expressed in Chinese, he'd handle them in English. Conversely, if some concepts can't be described conveniently in English, he'd use Chinese.
Do you know? Because of this ideology, last night I had to ask a Chinese student from Princeton to stay up all night to barely make me understand some of his ideas. I think in the future, Roth Dugan will be very frustrated, because Mathematics Annual might have to start accepting Chinese papers."
While saying this, Edward Witten pulled up Qiao Ze's email on his computer, then turned the laptop around and pushed it over.
Yang Xuanqing's full attention was immediately on the original email from Qiao Ze.
Sure enough, the entire academic discussion was in Chinese. This gave him a sense of familiarity as he was reading it.
After all, it was rare to see such pure Chinese academic reports at CERN, even the work emails were uniformly in English.
"In one spacetime, there are two spiral lines named 'Spira-X' and 'Spira-Y,' which together form a coordinate system. The coordinates can be represented as polar coordinates: [r_X(heta) = a_X \\exp(b_X heta)], [r_Y(\\phi) = a_Y \\exp(b_Y \\phi)]."
"Unlike the traditional Cartesian coordinate system, Spira-X and Spira-Y exhibit noncommutative properties, meaning their sequence directly affects the outcome of computations."
"This coordinate system requires redefining the operation rules to handle the rotation and twist of the spiral lines, with specific rules as follows:"
"This coordinate system has the following physical implications: 1, The rotation of Spira-X and Spira-Y is related to particle spin states; different spin states correspond directly to different rotational states of the coordinate axes."
"2, The twist of the spiral lines may affect the properties of space, causing the laws of physics in this coordinate system to differ from those in traditional three-dimensional space. For example, after introducing a twist function (f(r_X, r_Y)) and calculating, the propagation of light might exhibit peculiar behavior in this coordinate system. It is important to note that this twist function can be arbitrary, depending on the physical effects set."
"3, The relative motion of the two spiral lines involves changes in spacetime structure; calculations can potentially affect the rate of time's passage. The motion of certain coordinate points may cause local spacetime to bend and stretch, creating a spacetime structure that transcends traditional relativity."
"Below is the specific mathematical proof process... "
Yang Xuanqing didn't even finish reading the email before he couldn't continue.
The Fourier analysis formulas were already complex enough, but the spatial twist transformation formulas Qiao Ze presented were clearly even more complex and abstract.
In the email, Yang Xuanqing also saw the set of formulas Qiao Ze described on Weibo for the Containment Graviton. There was even the complete derivation process for the formulas; the only regret was that he couldn't understand these processes at all.
Especially since this space system allows for more degrees of freedom to model different physical effects. It seems quite useful, and from the effects, it should indeed be very useful. Otherwise, there would be no need for him to work overtime every day to prove the existence of containment gravitons.
But to Yang Xuanqing, these transformations seemed so abstract that they were beyond the comprehension of an average person.
For example, the "Invariance theorem": the value that remains invariant for any transformation or rotation in the coordinate system.
Obviously, invariance was another academic term coined by Qiao Ze, referring to a constant related to coordinate transformations in the Super Helical Coordinate System.
The specific mathematical expression is: In the Super Helical Coordinate System, for any moment (t), if there is a coordinate transformation ((x', y', z') = T(x, y, z)), then there is: [INP(t)=INP(t_0)].
Really, this was abstract enough to drive Yang Xuanqing crazy.
When he studied linear algebra in college, Yang Xuanqing thought those concepts were abstract enough, but they were nothing compared to what Qiao Ze presented.
The expression of the Twisted Connectivity Theorem left Yang Xuanqing utterly astounded.