A genius? I just love studying.

Chapter 107 A Conversation That Changed the World

"Young man, stop playing on your phone, the food's getting cold, it's bad for your stomach!"

The restaurant owner, wearing a white vest and with a white towel draped over his shoulder, sat on a bench in the first row, holding his phone and giving a serious reminder.

Chen Hui used to eat in the cafeteria, after all, this twice-cooked pork with potatoes cost 13 yuan a serving, which he couldn't afford before.

So the boss didn't know him; he just thought that kids these days don't study hard, they're always playing on their phones, and they don't even eat.

Each generation is worse than the last.

goooo...

Only then did Chen Hui temporarily emerge from the ocean of knowledge, only to find that his stomach was already growling with hunger, and was even aching from hunger.

I quickly grabbed a piece of potato and stuffed it into my mouth.

But the moment he put it in his mouth, Chen Hui frowned.

The food had indeed gone cold.

But I'm so hungry right now, I can't worry about that.

Before Chen Hui could even pick up a bite, the light in front of him suddenly went out.

The shop owner, wearing a vest and flip-flops, came up to him and said, "Let me warm it up for you."

As he spoke, the boss picked up Chen Hui's rice bowl and turned to walk towards the kitchen.

"thank you!"

Chen Hui thanked the departing figure.

The boss didn't answer, but soon the sounds of flames burning and spatulas busily moving about in the kitchen filled the air.

I never knew Mr. Yang Zhenning was so amazing!

While waiting for his food to heat up, Chen Hui's eyes went unfocused as he fell into thought again.

His intense research into Yang-Mills' theory had given him a deeper understanding of its proposer, Professor Yang Zhenning, and made him realize the significance of this Chinese scientist in the scientific community.

This is absolutely a scientific giant who can be compared to Einstein and Newton!
The Yang-Mills theory is an achievement at the same level as the law of universal gravitation, special relativity, and general relativity.

Even more impressively, Professor Yang Zhenning has another Nobel Prize-level achievement: the law of parity non-conservation!
Chen Hui had heard his classmates talk about this gentleman before. Of course, the classmates discussed the gentleman's private life. It seemed that no one was interested in his achievements. When they mentioned him, they did not express the same admiration as they did for Newton and Einstein.

He used to be like that too.

Until he truly understood the Yang-Mills theory.

To understand the Yang-Mills theory, we must start with the essence of physics: what exactly do physicists study?
There are all sorts of phenomena in nature, some related to the movement of objects, some to sound, light, and heat, some to lightning and magnets, and some to radioactivity, and so on.

Physicists then studied the underlying laws governing various phenomena, from Galileo's kinematic system to Huygens' wave optics, and Joule's laws of thermodynamics, each field forming its own system. And then were the physicists satisfied?
Of course I'm not satisfied!
Why? Because there are too many rules!

If every natural phenomenon were described by a specific law, how many separate laws would there be?
So physicists wondered, can I use fewer laws to describe more phenomena?
Is it possible for two phenomena to appear completely unrelated on the surface, but at a deeper level, they can be described by the same theory? Is it possible to eventually use a single theory to describe all known things?
This matter is essentially the same as Qin Shi Huang's unification of the six kingdoms. I will never allow the existence of six other independent states. Everyone must abide by the same laws, obey the same decrees, and use the same language and script. Only in this way can there be harmony.

The path to unification among physicists, which involved eliminating the "fragmented" disciplinary barriers, also began in this grand and sweeping manner.

Newton's law of universal gravitation was the first to unify the mechanics of the universe, incorporating the falling apple and the moon's orbit into the same mathematical system.

Maxwell's equations went a step further, incorporating electromagnetic phenomena into a unified theory and revealing the essential unity of electric and magnetic fields.

Breakthroughs in microscopic research in the 19th century revealed a deeper unity: macroscopic mechanical forces are essentially electromagnetic interactions between molecules, such as van der Waals forces; thermal phenomena are actually macroscopic manifestations of molecular motion, described by the Maxwell-Boltzmann distribution.

Thus, classical physics formed two pillars: gravity was described by the Newtonian system, electromagnetism was interpreted by Maxwell's equations, and the motion of matter was supplemented and improved by statistical mechanics.

The awkward thing is that Maxwell's equations and the framework of Newtonian mechanics are contradictory. So, is there a problem with Maxwell's equations or with the framework of Newtonian mechanics?
Einstein reconstructed the concept of spacetime through special relativity, successfully reconciling Maxwell's equations. Based on the unification of the principle of the constancy of the speed of light and the principle of relativity, he had to treat gravity separately, and proposed general relativity based on the equivalence principle.

Within the new framework of special relativity, Maxwell's equations can be directly applied without any modification; that is, Maxwell's equations are directly applicable within the system of special relativity.

However, some things in Newtonian mechanics cannot be directly applied, but can be easily adapted to this new framework with slight modifications. For example, the law of conservation of momentum. Directly using the definition of momentum in Newtonian mechanics is not possible, as momentum is not conserved in special relativity. It needs to be modified to be conserved, making it a second-class citizen.

There is another type of thing that, no matter how you change it, cannot be adapted to the new framework; these are troublemakers.

Troublemakers are a real headache, but thankfully, although they exist, there aren't many of them—just one: Gravity.

Newton's law of universal gravitation works well within the framework of Newtonian mechanics, but it is very rigid. No matter how it is modified, it will never submit to the new framework of special relativity. So what can be done?

Of course, physicists can continue to make changes. They believe that although gravity is currently unwilling to comply, they will eventually find a way to make it comply.

But Einstein took a different approach. He said that gravity was not going to change, so he proposed a new theory to describe gravity, essentially building a separate villa for it.

The new theory of gravity was extremely successful. Moreover, the way Einstein proposed this new theory was completely different from the way previous physicists had proposed new theories. This new approach brought about a dreamlike success that amazed physicists all over the world. Einstein was then hailed as a superstar. This new theory was called the theory of general relativity.

In the past, physicists conducted experiments to measure various data, then summarized the patterns, and used a set of mathematical formulas to explain these patterns. If the explanation was very good, then it was considered that the pattern of the phenomenon had been found, and then some properties hidden in the theory, such as a certain symmetry, were also discovered.

They followed a line of experiment-theory-symmetry, which aligns with our usual understanding.

However, Einstein reversed the process. He found that while the above method worked for simpler problems, it was disastrous when the problems became more complex or when experiments could no longer provide enough data.

For example, when Newton discovered the law of universal gravitation, Kepler summarized the three laws of planetary motion from the massive amount of astronomical data observed by Tycho Brahe. Then, Newton gradually guessed from this that gravity and distance are inversely proportional to the square, which was something that could be guessed so far.

But the upgraded version of Newton's theory of gravity, general relativity, is like this: How do you derive such complex equations from experimental data?

Moreover, in our daily lives, the results of general relativity are almost identical to those of Newtonian gravity. Tycho Brahe observed so much astronomical data that Kepler and Newton could guess the formula, but in the early 20th century, there was simply no data for Einstein to guess the theory of general relativity.
The perihelion precession problem of Mercury is one of the very few that does not conform to Newton's theory of gravity. However, when faced with this problem, people's first reaction is generally that there is an undiscovered asteroid inside Mercury, rather than that there is a problem with Newton's gravity, which has been used for hundreds of years.

Even if you believed at the time that it was due to the inaccuracy of Newtonian gravity, how could you possibly deduce the field equations of general relativity from such a piece of data?

After a series of setbacks, Einstein realized that when theories become complex, trying to deduce them from experiments is not feasible; experiments are unreliable. So Einstein sought something more reliable, and that more reliable thing was symmetry!
Symmetry can be simply understood as invariance. For example, the law of conservation of momentum has spatial symmetry, meaning it holds true at any location. Similarly, the law of conservation of energy has temporal symmetry, meaning it holds true at any time.

Experimental data may be unreliable, but symmetry is absolutely reliable!
Einstein thus revolutionized the way physics was studied, much like Copernicus. He first found a very reliable symmetry through observation and analysis, then demanded that the new theory possess this symmetry, thereby directly deriving its equations mathematically, and then using experimental data to verify whether his theory was correct.

Here, the original experiment-theory-symmetry becomes symmetry-theory-experiment. Symmetry has changed from a byproduct of the original theory to the core that determines the theory, and experiment has changed from the basis of the original inductive theory to a tool for verifying the theory.

So, after Einstein tamed gravity with general relativity and settled electromagnetism with special relativity, the next step was clear: unify gravity and electromagnetism!

Just like Maxwell unified electricity, magnetism, and light, explaining all physical phenomena with a single theory is the ultimate dream of physicists.

However, Einstein spent the rest of his life without being able to unify gravity and electromagnetism. Moreover, with the advancement of experimental instruments, Rutherford's atomic model revealed the existence of the strong nuclear force, followed by Hideki Yukawa's meson theory to explain the nuclear force, and Fermi's theory of weak interactions.

These findings indicate that there are four fundamental interactions in nature: gravity, electromagnetism, the strong force, and the weak force. However, gravity and electromagnetism have not yet been unified, and the strong and weak forces also operate independently.

Now, not only have we failed to unify gravity and electromagnetism, but two new forces have emerged.

Gravity is described by general relativity, electromagnetism by Maxwell's equations, and the strong and weak forces are still unknown, let alone their unification.

At this point, the Yang-Mills theory came into play. Its non-Abelian gauge symmetry provides a mathematical description of the strong interaction. Through the SU(3) group gauge field, the Standard Model further unifies the weak force and the electromagnetic force into the electroweak force. Through the breaking of the SU(2)×U(1) group gauge symmetry, it finally forms the framework of the four fundamental forces in current particle physics.

In other words, of the four fundamental forces, apart from gravity, the other three are described by the Yang-Mills theory, so the importance of the Yang-Mills theory is self-evident!

Chen Hui used to think that what scientists did was abstract and unrealistic, but today he discovered that scientific research is actually quite interesting!
If the shortcomings of the Yang-Mills theory can be resolved, the unification of electromagnetic force, strong force, and weak force will be achieved.

Just thinking about it makes Chen Hui excited!
"Alright, let's eat it while it's hot this time!"

The sounds of burning in the kitchen and the clanging of spatulas against iron pots had stopped. The shop owner placed a twice-cooked pork with potatoes that had been reheated in front of Chen Hui.

Woohoo...

Chen Hui's phone vibrated, and he instinctively reached for it.

The shop owner's eyes widened immediately.

Chen Hui withdrew his hand somewhat embarrassedly, feeling awkward about asking the owner to reheat the food again.

It probably wasn't anything important, otherwise they would have called.

With this thought in mind, Chen Hui picked up his chopsticks and began to eat voraciously, like a hungry tiger pouncing on its prey.

I must say, although this shop is small and has a run-down industrial style, the twice-cooked pork with potatoes tastes really good!
I'll definitely come here to eat more often when I have more money.

Seeing this, the owner finally felt satisfied, slipped on his slippers, and returned to his seat in the first row of tables to start playing on his phone.

After eating and drinking his fill, Chen Hui finally picked up his phone.

It was a message from Fang Wen.

“Great God, I know you are exceptionally talented, but the Millennium Problem is still too difficult. You know Fields Medal winner Qiu Chengwu, right? Back then, his teacher Chen Xingshen wanted him to study the Riemann Hypothesis, but he was very aware that it was a huge pitfall and did not do so, otherwise he would not have won the Fields Medal.”

The best example is Zhang Yitang, who studied the Riemann Hypothesis. After graduating with a PhD from Purdue University in 1992, he accomplished nothing and could only wash dishes in a restaurant. It wasn't until 2013, when he published the twin prime theorem, that he gained recognition in the academic community, obtained a university teaching position, and turned his life around.

He was lucky; countless geniuses plunged headfirst into the Millennium Problem and never emerged.

I think you can start with something simpler.

Fang Wen always remembered Chen Hui's kindness. He couldn't bear to see such a genius live a mediocre life because he chose the wrong path.

"If you want to make money, combining mathematics with other disciplines to make applications is also a good choice. For example, mathematics + physics. The recently popular condensed matter physics can be said to be the most popular topic in the field of physics. Mathematics is the basic language of this topic. Experts can give full play to their talents."

Do you remember the infamous "stealing China's superconductivity" fiasco a couple of years ago? One of the main research directions in condensed matter physics is room-temperature superconductivity. If a major breakthrough can be made, it could be more profitable than solving the Millennium Problem.

You know about controlled nuclear fusion, right?

The most crucial structural element, the tokamak device, requires superconducting materials. If room-temperature superconductivity can be achieved, the key technological challenges of the tokamak device will be solved. Then, controlled nuclear fusion and seawater power generation will be possible, generating more money than you could ever spend!

As Fang Wen spoke, he seemed to get a little excited and started to go off-topic. Fang Wen himself could not have imagined how much his words would change the world.

However, Chen Hui did take it to heart, "Condensed matter physics?"

He wasn't a fanatical person, although he believed that as his proficiency improved, the Millennium Problem would be no problem if he was willing to delve into it.

But nobody knows how much longer it will take.

Before going here, you can certainly study other topics first, as this will also improve your mathematical proficiency.

He was also somewhat tempted by the vision Fang Wen described.

That's controlled nuclear fusion!

If this breakthrough can be achieved, the world will be changed!
"Since it's mathematics in condensed matter physics, let's study condensed matter mathematics first!"

(End of this chapter)