Tech Hammer

There is actually a very deep relationship between mathematics and physics. For example, both disciplines are very ancient. Generally speaking, excellent physicists are often also excellent mathematicians, such as Newton and Einstein. The reason is naturally very simple. , Physics research is based on mathematics. If you don’t understand mathematics and rely on imagination to study physics, it is nonsense.

However, in terms of specific research, especially in modern science, the research methods of the two are actually different. The reason is also very simple. With the development of mathematics today, many branches have tested the abstract thinking ability of geniuses, while physics has always been a subject that studies natural phenomena. To put it simply, to study mathematics, you only need a notebook and a pen to build an imaginative world.

Algebraic topology, algebraic geometry, algebraic number theory, category science, etc. are actually more than just the knowledge of "numbers", but the abstract study of relationships and structures.

But physics is about studying specific things. Whether it is classical physics, quantum physics, celestial mechanics or condensed matter physics, no matter which direction it is, the ultimate goal of physics has never changed, and that is to study all the laws of motion in the material world. Find the essential reasons behind those strange natural phenomena.

Therefore, many times physicists first observe a certain natural phenomenon, and then begin to explore the reasons for the occurrence of this phenomenon, find out the rules, and use mathematical tools to describe their research results, and at the same time use mathematics to quantify them.

For example, Newton observed the action of force and creatively proposed the theory of universal gravitation. However, this was not enough because words could not accurately express this theory. So this genius creatively invented calculus, which gave countless mathematicians a headache, to accurately describe this theory. A theory; another example is Maxwell's invention of field-shaped matter - electromagnetic waves and light waves, and later generations introduced the mathematical fiber bundle theory to accurately describe it; and then Einstein proposed the general theory of relativity and discovered gravitational waves. At this time, it is necessary to Riemannian geometry came to make people realize the correctness of general relativity.

In the end, one of the dark clouds in physics was the emergence of quantum physics. At this time, scientists discovered that quantum physics can be based on linear algebra. In other words, if you really want to understand quantum physics in depth, you must first pass the linear algebra level, because when you open those quantum physics textbooks, you will find that various mathematical matrices and mathematical physical equations often appear, and It’s not just to tell you how counter-intuitive the double-slit interference experiment is, or how amazing quantum entanglement is. That’s popular science, not science.

In this way, every major revolution in physics is joined by a new mathematical theory, and the two are therefore inseparable.

Fortunately, for Ning Wei, when the three words physics came to his mind, mathematics was definitely not the threshold that hindered his research. And theoretically speaking, he is more qualified than anyone else to explore the truth of physics.

Even though physics has now developed to a very high level, and various fields have embarked on a path of subdivision, the most mainstream research directions are still two major categories, macro and micro. Of course, judging from the current development trend, more attention is paid to the microscopic level, especially quantum information and multi-qubit entanglement, because there is not even a complete mathematical theory that can describe or even name multi-body quantum entanglement.

From this point of view, it is somewhat debatable that Google has directly announced that its quantum computer has led the world and has mastered quantum hegemony.

Of course, the greatest ambition for physicists is still to establish a grand unified theory that unifies all the four basic forces that affect nature, namely the strong force, the weak force, the electromagnetic force and universal gravity, and to establish a standard model to explain all the basic forces in the universe. The particles interact with it.

Obviously this goal is still far away, and it is still unknown whether there is such a basic theory. Because even if modern physics has developed to the point where many people are intimidated, the nature of gravity is still vague. Neither Einstein’s gravitational wave theory nor the predicted but not yet discovered gravitons seem to be enough to convince everyone. Everyone is convinced.

A very complex subject.

But Ning Wei felt that if he wanted to understand the meaning of this inequality seriously, he still needed to study this complex topic. There is no doubt that this path is most likely correct, because in another parallel universe, this inequality was proposed by a Chinese quantum physicist and was named Ma Zhenhua's inequality.

Of course, despite the fact that this inequality is very simple, based on people's current understanding of quantum mechanics, it would take thousands of pages to explain this inequality clearly and form a paper.

For Ning Wei, he is just looking at the inequality with the eyes of a mathematician, and through some mathematical logical judgments, where should he start to analyze the inequality and find a way to solve it.

Then quantum physics came to mind again.

Well, that's pretty good. Speaking of which, Ning Wei has a basic understanding of quantum physics. This understanding was due to the fact that he went to the library to rent a book on the history of the development of quantum physics when he was at Jiangnan University... and had a thought in his brain. Storm, as if experiencing the changes of the universe as a bystander, saw the magnificent and magical scenery at the micro level.

But Ning Wei feels that his intuition makes sense. In fact, the micro level is actually very interesting. For example, scientists once thought that atoms were indivisible. After scientific development, especially the advancement of equipment at the microscopic level, they realized that atoms are not the smallest unit of particles. Atoms also include a nucleus and extranuclear electrons. At the same time, the nucleus is composed of protons and neutrons. constitute.

When scientists at that time believed that protons were indivisible elementary particles, the Large Particle Collider appeared and discovered that protons could also be subdivided and were composed of quarks and gluons.

When these concepts appeared in Ning Wei's mind, he had already figured out the movement diagram of particles in the microscopic world. From a human perspective, the movement trajectories of particles cannot be completely determined and can only be expressed in terms of probability, but maybe in the microscopic world At the same level, if we slow down time, slow it down, slow it down again, and slow it down to Planck time as the unit for observation, will the dynamic picture presented in the microscopic world at that time be similar to the way humans observe the universe now?

The layman's imagination lasted for about three seconds, and then Ning Wei opened his mouth and said to March, who was bored and cute on the computer screen: "Help me sort out a set of recognized knowledge systems of quantum mechanics. What books do I need to read in the first place? Theoretical books on various branches of research, as well as the most cutting-edge valuable papers, were all sorted out for me. It seems that I need to study again."

Organizing information is undoubtedly what March is best at, and she would rather be ashamed of it.

This is thanks to the fact that although the specific researched technologies are hidden deeply by everyone, physics in the world can still maintain interoperability at least in theory. Of course, this is something that cannot be helped. The progress in theory requires the thinking of scientists. Of course, more importantly, it is impossible to judge whether many theories are right or wrong before they are verified. Everyone needs to pool their wisdom to study, and naturally there is no need to hide them.

Of course, once a theory is connected to practice and produces results, it will generally become a secret that is not passed down. Especially in physics, generally speaking, physicists who study applications have more money than most who study theory, because Application is relatively easy to produce results; but for theoretical research scientists, the life trajectory is directly the difference between 0 and 1. The vast majority of theoretical physicists are 0. They devote their lives silently, and even few of them die. Knowing their names, only a very small number of people can become No. 1, directly recorded in history, and even use their names as units of measurement.

Of course, this does not mean that those 0s are meaningless. In fact, many times the research on those 0s paves the way for 1s, or inspires them. This is also the reason why the world of theoretical physics cannot accommodate too many people. It is too harsh to take advantage of talent...

In particular, the study of physics has its own peculiarity, that is, it is too easy to get started. Especially high school physics is very interesting and can easily get people into it. For example, after studying high school physics and understanding some basic mathematical knowledge, you can easily understand why a large truck running at the same speed is more difficult to stop than a small car, and you can also easily understand why one light can use two switch to control.

Not to mention that the physics knowledge in middle school and high school also involves many interesting experiments. As long as you understand the principles and spend a little thought to make it, it is no different from a small toy made by yourself. It is still a wonderful and counter-intuitive thing. , it is easy to become addicted to exploring these novel fields. For example, the science museum we went to in junior high and high school has many very strange devices made using simple physics knowledge, such as a homemade phonograph.

But it's completely different when you get to college. The physics you start to study in college are basically invisible in life, and are replaced by many cumbersome formulas. It even makes people think that high school physics and college physics are not the same subject at all. What is tested at this time is abstract ability.

When searching in March, Ning Wei had already gone through the physics knowledge he learned in high school in his mind, and he went through it very vividly. Light, atmosphere, electricity, electromagnetism...

Ning Wei felt a little excited about re-investing in a brand new research and study. For him, this is a new beginning. And it starts with the assistance of artificial intelligence.

March also showed its ability. After Ning Wei systematically sorted out the physics knowledge in his mind, March also compiled a catalog of physics textbooks according to his needs.

Ning Wei clicked on the catalog and arranged the "General Physics" course in great detail, including basic mechanics, heat, electromagnetism, optics and the history of the development of modern physics, and then a series of the development history of particle physics. After studying particle physics After that, he came to the quantum physics that he needed to learn. The only reference books given were "Introduction to Quantum Mechanics" and "Principles of Quantum Mechanics". Then there were a lot of lectures and papers. Ning Wei looked at the papers he needed to know. Directory, 386 articles were recommended to him in March...

"On what basis are these papers recommended to me?" Ning Wei asked.

This question is necessary because Ning Wei knows very well that even with March's ability, it is impossible to browse nearly 400 papers at the same time in such a short period of time and determine the value of these papers.

But soon March gave a well-founded answer: "Meow... This is taken from the ranking of outstanding master's and doctoral dissertations in the top 50 universities in quantum physics in the past ten years."

This answer is very convincing.

Although the review of his doctoral thesis was a bit sloppy, for the vast majority of doctors, no matter how watery a small thesis is in the doctoral research stage, it will not be taken more seriously than a large thesis. Especially for prestigious schools, large papers generally use double-blind review. , even in China, regulations are becoming more and more strict. For example, many doctoral programs have begun to prohibit the listing of published small papers, and even the names of journals and conferences in graduation thesis.

This is actually because the doctoral thesis is also one of the most important masterpieces in life for many serious doctors. After all, if the paper published in the journal is not well written, it can be revised, but if the doctoral thesis is passed, it is finalized and there is no need to re-write it. Take it back and write it once, and many graduate students who are new to this field will first read the doctoral theses left by their predecessors to enter this field. Therefore, serious doctoral students in prestigious schools generally attach more importance to their graduation thesis.

When making citations, you will naturally check the evidence again and again, and you will definitely not use some research conclusions with no quality at all in inferior journals. So this screening mechanism is undoubtedly extremely scientific.

"Okay then, go ahead." Ning Wei waved to Sanyue, then took a piece of paper and copied down the required bibliography. He stood up and walked out of the office, just in time to see walking under the stars. When Jiang came, a smile appeared on his face unconsciously. He casually put the required bibliography into the hands of Liu Wei, who was leaning against the wall, and then walked towards him.

"How was your review today?" Ning Wei asked.

"Huh... I just finished the Western microeconomics study question set." Jiang took a long breath, and then smiled happily. From this smile, it can be seen that the academic pressure at Yanbei University is extremely high after all. big.

"Well, that's good. Congratulations to Mr. Jiang for taking another step towards becoming a great economist in the future." Ning Wei congratulated formally.

"Don't make trouble, you economist. I'm exhausted from all the concepts in optics." Jiang said with a blush, and looked up at Liu Wei, who was standing at the door of Ning Wei's office. Fortunately, Liu Wei Brother was looking at the piece of paper that Ning Wei had just pushed to him, looking a little dazed. He probably didn't hear what this guy said.

"Look, it's superficial, right? When I tell you about economics, just memorize more nouns so that you can fool people when doing research. Anyway, there are only two situations in judging the future economic situation. Either is wrong. , either right, as long as the analysis is correct a few times, isn't it an economist? It doesn't matter if it is wrong, anyway, all the conditions of this thing are fictitious, and there are many people who come to the opposite conclusion under the same conditions, who would do it? Are you really serious with me?"

Ning Wei said unconvinced.

"There are still a lot of scientific truths, okay? How can I talk nonsense? Are you done with your work today?"

"Well, I'm ready to go back at any time."

"Wait a minute, let me clean up the office for you first. I haven't been here for two days and it must be in a mess again."

"Actually, it's not bad...Okay...I'll wait for you then."

Classmate Jiang smiled and said hello to Liu Wei at the door, then walked into the office and started to clean up. Liu Wei also raised the manuscript paper in his hand, looked at Ning Wei inquiringly and asked: "Professor Ning, what are you... …”

"Of course I just need these teaching materials."

"No, I mean are you going to start studying physics?"

"Well, you told me that I should wait for this world. I think what you said makes sense, so I decided to start studying physics from the beginning, so that I can relive the feeling of being an undergraduate and systematically learn a new subject. Knowledge. By the way, I don’t know. I’m already a professor. Can I still get a double degree at the undergraduate and master’s levels?” Ning Wei sighed.

Liu Wei held the piece of paper, thought about it in his mind for a moment, and said pertinently: "If you just want a double degree certificate... maybe you don't need to go to such trouble."

Ning Wei stood at the door and watched classmate Jiang neatly tidy up his messy desk. His mood became inexplicably good, and he explained casually: "Haha, you are just kidding, Brother Liu, I know it too. It's just you. I don’t know. My biggest regret in my life so far is probably that I didn’t take the postgraduate entrance examination or the Ph.D. examination, so I always miss my undergraduate stage. Of course, I can’t really take the exam again. At most, I can visit and listen to lectures occasionally. The main thing is that I I have become somewhat interested in physics. I feel a little tired from doing math research recently. Reading a physics book is like reading Cologne when you are free. It can rest your brain."

"Oh..." Liu Wei nodded, indicating that he believed Ning Wei's explanation. In fact, Ning Wei didn't need to explain anything.

"No, do I need to worry about studying physics?" Ning Wei finally looked away from the graceful figure and looked at Liu Wei and asked.

"how to say……"

Liu Wei thought for a while and then said: "When I saw this piece of paper, I suddenly thought of what my high school physics teacher said in the last class before the college entrance examination. He said that the most important thing for us to learn physics is thinking, and The imagination is not simply limited by the theories in books. The theories in physics are actually constantly being revised, just like Newton's law of universal gravitation is revised by the general theory of relativity. So the teacher hopes that some of us will study physics in the future. You can also become a scientist who corrects previous theories."

"Of course, the physics teacher also said that if you want to revise or even overthrow a theory, you must first study and understand the theory in depth before you can be qualified to comment on the current theory, so he sent a message to all aspiring students in our future class Children who are interested in studying physics can become real scientists instead of dreamers. Thinking of this sentence, I suddenly feel that when you read these physics contents, you don’t want to..."

Ning Wei looked at Liu Wei in surprise and said, "Brother Liu, if you, a high school physics teacher, can say these things, your teaching level must be very high, right?"

Liu Wei nodded and replied: "Well, he has always been a teacher that I respect very much. In fact, he has the same message for every student he has taught. It's just a pity that for now, we all let He was disappointed."

"Oh, then bring two copies of these textbooks and one for you. We can study together. If you don't understand anything, you can ask me. You protect me and I will take you flying." Ning Wei was very happy Understanding patted Liu Wei on the shoulder and said.

"Um?!"