"Good afternoon, ladies and gentlemen. Today, I'm going to explain some of the concepts of the field. I know you probably get a big head when you hear this name, and that's normal. Truth be told, so am I. Don't be surprised, the core general relativity and gauge field theory related to field theory seem to me to be almost one of the two catastrophic breakthroughs of the twentieth century. For there is no doubt that they reveal to us a path that may be right but is incomparably dark, the principles of which cannot even be fully grasped by the human mind alone. Here's the scariest part, and if they're correct, there's nothing wrong with imagining God as a nasty programmer who loves Monte Carlo simulations. But fortunately, we are not going to explain the content in detail today, just to give you a conceptual understanding of it. ”

"Really, why did I come to Kaihara-san's counseling meeting?"

Kuroko Shirai sat in the audience and muttered to herself while taking notes.

"Don't complain, if you hadn't missed the class, it wouldn't have been. Anyway......" Mikoto Misaka looked left and right, "I really didn't expect so many people to participate......"

Indeed, the audiovisual classroom was almost three-quarters sitting. For Tokiwadai, which has a total student population of only about 200, this number is quite staggering. And what's even more incredible is that there are some teachers among them.

This is probably what makes the Dome special. Although the content of her lecture does not involve too complex mathematics but only conceptual things, and the physics teachers do not pay much attention to the content, the teachers of other majors are still happy to come and learn about the knowledge of physics.

In fact, this tutoring is mainly to make up for some of the courses they have taken for some students who have missed the course. Originally, this work was done by the teacher, but today, the teacher in charge of lecturing was on leave, so Tokiwadai pushed the dome out.

It seems that this is about to become a regular occurrence.

“…… The existing Standard Model of particles is based on the Chen-Ning Yang-Robert Mills gauge field theory. Since the load it describes does not obey the law of multiplicative commutation, it is also known as a "non-abelian gauge field". At this point, perhaps students who have a concept of quantum mechanics can think of quantum mechanical variables, but there are some differences here. Because this is not the result of quantization, on the contrary, in classical theory, it is represented by a matrix. ”

The inspiration for this came from an idea that seemed almost completely unfounded at the time. If Yang Zhenning is more talented than others, it is that he has found the answer to this question with his keen physical intuition. It is believed that an action field can be conceived and described in a theory similar to that of an electromagnetic field. Just as the electric current formed by the movement of an electric charge creates an electromagnetic field, and the field can act on a distant charge and an electric current, this similar field is used to deal with nuclear forces. This is the Young-Mills canonical field. Yang Zhenning and Robert Mills geniusly conceived a charge called 'isospin', and used the 'localized normative invariance' of classical Maxwell's theory to make a far-reaching generalization, resulting in a new equation that is now known as the Yang-Mills equation. This is where gauge field theory comes from...... Misaka-san, do you know what the most basic and simple normative field is? ”

"Huh? Ay? ”

Because she didn't expect Qiongno to call herself, Mikoto, who didn't pay attention to it at all, was dumbfounded on the spot.

Dome sighed, she just saw Mikoto's absent-mindedness, so she deliberately asked her. Of course, just to remind her that there is no intention of chasing and fighting. Seeing that she had already reflected, Dome continued to speak.

Actually, the answer is already included in what I just said. The most basic and simple gauge field, that is, the electromagnetic field that you are most familiar with and understand. ”

Mai Trin sat down with a red face, this time she didn't dare to wander anymore. Although the dome is generous, it is relatively strict at this moment.

"We know that the point of view of the field is now used to describe nuclear forces. Yang's paper was published in 1954, and although all physicists knew about its importance, no one paid much attention to it at the time. This is not surprising, given that at the time, the physics community was generally pessimistic about describing nuclear force in terms of fields. In fact, this is not an accident, at the time, there were still too many problems that had not been solved. Fortunately, after more than ten years of hard work by several famous physicists, most of them have been solved, allowing us to describe different charges in the same mathematical form. By the '80s, everyone was surprised to discover the fact that three of the four fundamental forces in nature were described in terms of the Young-Mills field. Clearly, the Young-Mills gauge field theory proves in a very obvious form the possibility of a fatal attraction, which is that all four fundamental forces are probably the same in nature. One can imagine how excited physicists were when this was discovered. ”

"It's interesting that all the theories of the existing Standard Model have the same basic principle, which is normative invariance. The term normative invariance may sound exaggerated, but the most basic idea is simple. In fact, there is something problematic about the term normative invariance itself. Actually, the name should be "local phase invariance". Let's get acquainted with the most basic double-slit diffraction experiments. This is the interference fringe caused by the diffraction of the double slit that we are familiar with, and now we insert a thin slice behind the two slits and the interference pattern changes because this flake changes the phase of the electron waves passing through it. Okay, now notice that if the phase change of the waves coming from the two slits is the same, the interference pattern will not change. This is one of the invariants of the double-slit experiment. Because the only effect of the lamellae on the electrons is that it causes a phase shift in the electron wave, this property is called 'phase invariance'. ”

"It is important to note that this invariance has a peculiarity that the inserted sheet must cover all areas. If we just insert a sheet behind one of the seams, the interference pattern changes. It's easy to understand. Note, however, that there is a way to make us change the phase locally while maintaining the invariance. Since the magnetic field can cause a change in the trajectory of charged particles, it is possible for the local phase to remain unchanged. In other words, we can insert a thin slice behind a slit but introduce a magnetic field at the same time to maintain the invariance. This theory brings a key hint - if we don't know how electrons and photons interact and need to satisfy local phase invariance, then we have to introduce a magnetic field and have it interact with electrons in a specific way. In this way, we have a theory known as QED (Quantum Electrodynamics). It is the product of the quantization of Maxwell's electromagnetic field and is the forerunner of all gauge theory. In a similar way, we can learn about canonical particles by the requirement of local phase invariance. This is why gauge field theory is the theoretical basis of existing particle models. ”

"The gauge field theory, which is currently the most successful theory known to mankind, deals with the electromagnetic, strong and weak interaction forces in the same way, which is the greatest proof that these three are essentially different manifestations of the same force. However, it has a very big limitation and that is that it cannot handle gravity. ”

"Yes, such a successful theory, but unable to deal with gravity. Although it successfully deciphers three of the four forces in nature, gravity cannot be dealt with by gauge field theory. Gravity is determined by a completely different set of theories. This theory is familiar to us, which is Einstein's immortal general theory of relativity. ”

"We know that gravity is defined in general relativity as the result of mass causing space-time to bend. This definition cannot be applied to gauge field theory, which is a difficult problem in coordinating the two theories. This is a very sad thing. While we can almost be sure that all four interacting forces in nature are essentially the same, the gulf between general relativity and gauge field theory seems insurmountable. Does this mean that we are at a loss? No, it's not like that. ”

"In the existing physical theories, the description of space-time is not universal. A large part of this is due to the fact that physical theories themselves are not universally valid. As far as we know, in many areas, general relativity and quantum mechanics are not in harmony. It's like a Scrabble game, even if you change just a few words, it will cause the whole word to change. Luckily or unfortunately, perhaps we've found the right point of convergence. ”

"Opportunity, in general relativity. If we expand Einstein's field equation according to a weak approximation, we will find that we have the equation of motion of a light-speed particle. This is where quantum mechanics and general relativity come in, and it's called a 'graviton'. In this way, we will quantify gravity and try to deal with the pain points. The specific content of this cannot be explained clearly in a few words. But the conclusion, which we are very familiar with, is the theory of supersymmetric strings and the theory of quantum gravity - it should be noted that these two are likely to be different manifestations of the same theory. ”

"Supersymmetrical string theory has a lot of difficulties. One of the difficulties is that for it to make sense, our space has to be eleven dimensions – yes, the way in which the spatial capables move. It's quite remarkable. Among us here, there is a student who is good at this. ”

At this point, Dome paused and nodded to Shirai with a smile. Suddenly, everyone's eyes were focused on Kuroko Shirai. Even if she has always been known for her cheekiness, she is a little embarrassed.

Although she may seem a little self-righteous, she is self-aware. Her ability, in fact, does not apply much to string theory itself. In fact, she first assumes the eleventh dimension without self-evident and then applies empirical formulas that have been proven to work. What is applied is only the conclusion of the spatio-temporal structure of the string theory, and it is not at all as remarkable as the Dome says.

This wasn't unique to her, as far as she knew, it was true for all spatial abilities.

"It should be mentioned here that in order to maintain the supersymmetry without being destroyed, it is necessary to apply the compaction of the Kabila-Yau Chengtong flow pattern. This concept is more complicated, so I won't mention it here. In fact, in the eleventh dimension, in addition to our common four dimensions of time and space, there are six dimensions that are curled up in the Kabila-Yau space. They are curled very small, and according to this theory, every point around us is such a Kachu space. I'm not a spatial person, so there's no way to imagine it. However, perhaps this is the reason why spatial ables are able to move point-to-point. ”

After saying that, Qiongno looked at Kuroko Shirai for a while, as if he wanted to learn something from her. However, it is a pity that Shirai Kuroko himself does not know the answer, so he can only shake his head apologetically and answer.

Although Qiongno did not get any valuable answers from Shirai Kuroko, it did cause some associations with Shirai Kuroko.

In the gymnasium accident two months ago, Kuroko Shirai tried to use her abilities on Qiongno, but nothing happened. In other words, for some reason, her spatial movement ability could not be applied to the dome state, which was something she couldn't figure out.

(Time curl...... Gravitation...... Graviton...... Spacetime...... Umihara-san's ability seems to be the control of the gravitational field? Could it be that the reason for the ineffectiveness is here? ）

Shirai spun his pencil and thought wildly in the unknown.

I don't understand......