Super God-Level Top Student-Chapter 1091 - 427: All Regretful?

"Professor Witten, could you explain the integration invariance under different metrics g in the mathematical intertwining formula I(ϕ) of Q theory? Specifically, if we integrate under Riemannian and pseudo-Riemannian metrics, should the results be the same? If they differ, how do you maintain theoretical consistency?"

From the podium, Edward Witten, who had just finished his presentation, looked at Critiel Matich with a slight headache.

During the Q&A session, when he saw Matich raise his hand to ask a question, he signaled the host to call on him. After all, they were old rivals, and it felt incomplete not to have a little verbal spar.

But now he even thought to himself that he should not have sent an invitation to this stubborn guy. As expected, this guy was always thinking about how to play the opposite. Looking for loopholes in the theory he supported.

But there was no choice; the question was indeed tricky. It belonged to one of the problems in Q theory that hadn’t been fully explained.

The logic was simple. It was inherently complex to address pseudo-Riemannian metrics. The reason is that in the original design of Q theory, the metric affects not only the spatial part but also the temporal part, and it directly changes the overall form and result of the integration.

However, to solve a series of problems in Q theory, Qiao Ze removed the time dimension from the theory. This led to a significant increase in complexity in maintaining theoretical consistency under different metrics.

Yes, the world is sometimes strange this way. A subtraction on a large scale, but additions or even multiplications appear on a smaller scale. Fortunately, he had argued with Peter Schultz about this issue, so he wasn’t completely at a loss.

"I have to say, Professor Matich must have studied Q theory closely recently, presenting a very good question and a complex challenge we face in our research. Today, I can only try to answer this question.

First, the mathematical intertwining formula I(ϕ) indeed depends on the metric g, because the volume element dμ and the function F(ϕ,g) are directly related to the metric. Under different metrics, the results of integration are generally different.

For example, in standard Riemannian geometry, the choice of metric affects the value of the integration. In spaces of different curvatures, the volume element and the corresponding integration result will differ, which is common knowledge.

As a theory attempting to solve the grand unification problem, Q theory indeed faces the test of pseudo-Riemannian metrics, such as spacetime metrics in general relativity. To maintain theoretical consistency under different metrics, it usually requires introducing some invariants or gauge adjustments. These adjustments aim to maintain the physical significance of the formulas under different metrics unchanged."

Within the framework of Q theory, we have considered some possible adjustment methods, including introducing gauge fields or additional symmetries, to ensure the physical consistency of integration results under different metrics. For example, adding compensation factors in the integration, but these adjustments are still under research, and there isn’t a completely resolved method yet.

This is also why we publish papers and invite everyone to the conference. Indeed, Q theory is not mature yet. Even within our internal discussions, there are still many debates between me and Professor Schultz.

At the same time, this also proves once again that we need experimental data to verify if these theoretical adjustments are correct. Thank you very much, Professor Matich, for this question, I also hope you can help us in the future work to modify Q theory, thank you."

After speaking, Edward Witten looked at Critiel Matich standing below. According to this guy’s usual behavior, he expected a vague explanation would lead Matich to sarcastic remarks, but surprisingly, today, the usual contrarian didn’t show a disdainful expression.

He merely paused for a moment and then formally said, "Thank you for your detailed response, Professor Witten. It seems this is a very complex issue. I hope you can make breakthroughs in your subsequent research."

Then he handed over the microphone.

Truly, this series of actions even sparked a slight sense of guilt in Edward Witten. fгee𝑤ebɳoveɭ.cøm

Because in his mind, Qiao Ze’s words echoed: "Through my observations in life, the reason why fools’ voices often seem louder is that they enjoy showcasing their presence in various occasions."

Although a Nobel laureate is certainly hard to associate with foolishness, but... who isn’t?

In short, Critiel Matich’s unusual behavior made Edward Witten feel a bit uneasy, so at the luncheon of the conference, he approached again proactively.

The luncheon was in the most convenient form of a buffet. Simply put, a self-service meal. Unlike purely Western-style buffets, there were also many Chinese hot dishes, catering more to the taste and appetite of domestic scholars.

Such an arrangement’s greatest advantage is mainly facilitating free interaction among the scholars attending.

The dining hall of the Mathematics Research Institute was large enough for familiar individuals to freely find a place to sit together.

After arriving at the cafeteria, Edward Witten took his meal, greeted several familiar scholars, chatted a bit, then walked around the hall, and soon saw Critiel Matich and a young man sitting at a window-side table in the southwest corner, enjoying a steak, so he went straight over.

"May I sit here?" Edward Witten politely asked.