Chapter 249 Lin’s wave coherent superposition equations

For Lin Xiao, or for the physics community, it is obviously incredible that interference and diffraction can be related to strings.

Of course, although it was unexpected, it was also reasonable.

The wave function is the function that describes de Broglie waves. It is also the so-called material wave. It refers to the probability that matter may appear at a certain point in space at a certain time. Of course, this [matter] often refers to microscopic objects. It does not mean that A person may appear in another place at any time and at any time.

For string theory, the wave function is a basic tool for analysis, so linking string theory and waves is a very reasonable thing for Lin Xiao's current research.

Of course, it was not an accident that he connected the two, because when he performed topological analysis on the interference and diffraction space of waves, he was surprised to find that he could connect string theory with it.

Of course, this connection is not close, it is just a connection between a few unknown numbers. However, when he tried string theory, he did not have such expectations, because he felt that Found it to be a bit too simple.

However, after trying it, he finally discovered that it was really that simple.

In the formula he finally obtained, the algebraic formula representing the basic string actually controlled the process of wave diffraction and interference.

If this inference is posted on arxiv, it will probably cause a lot of people to speculate.

Of course, before that, Lin Xiao felt that he needed to do more research.

For example, verify this finding in another way.

Therefore, he analyzed this problem again from the perspective of algebraic geometry.

However, in the process, he encountered a little problem.

"How do I convert this function into modular form?"

After thinking for a moment, something suddenly came to his mind.

He thought of something he once proposed.

Lin's guess.

Lin's conjecture points out that any function can be converted into a layer form.

Of course, no one has been able to prove this problem since Lin Xiao proposed it at the International Congress of Mathematicians in 2018.

Just as Professor Deligne thought at the time, it would take at least twenty years to solve this conjecture. This problem is difficult enough.

And if Lin Xiao can prove this problem, he can convert the function in his hand into a layer function, and then easily convert it into modular form.

Of course, this is really overkill.

He doesn't have the time now to solve this Lin's conjecture.

"However, if it is in mold form..."

Lin Xiao fell into thinking again.

This problem must be solved. If it is not solved, he will not be able to verify that string theory is related to the diffraction and interference of waves.

This is like a P=NP problem. Substituting string theory into it is P, and he is now deriving this result from the general method in reverse, which is NP.

Obviously, this is difficult.

The pen tip rotated on the paper, and mathematical formulas flashed along with Lin Xiao's thoughts, gradually filling the paper.

No matter what, what Lin Xiao likes to study most is this kind of theoretical problem.

Research in applied disciplines requires running around and doing various experiments. He seems to be quite tall, wearing a white coat and holding a test tube in his hand.

It's a pity that Lin Xiao doesn't think that is his style of painting. Holding a pen and facing a piece of paper with complex mathematical formulas, that is the style of painting that he thinks he should have.

Of course, if necessary, he would still change into a white coat and hold a test tube in his hand.

Just like his current job, he is actually striving for the painting style of white coats.

There was no time to think about these problems. As Lin Xiao calculated, he finally found the method that could solve the problem from a certain corner.

"A new form can be created by subjecting the original function to a special transformation. By multiplying this new form with a simple matrix, the modular form of the original function can be obtained. Hmm...it seems like an accident. Is it a bit complicated?"

Lin Xiao looked at the formula in his hand and the various physical quantities in it. In his eyes, these were just things that represented complex mathematical relationships.

However, in order to solve his problem, he still made a little fuss and directly created a new mathematical form, which is probably like a modular form, a new form of mathematical expression.

Of course, his new mathematical form is very closely related to the modular form. It is probably equivalent to the companion form. It can be transformed into the modular form after simple transformation. However, its role is not limited to this; relations between modular forms and other mathematical forms.

Just like now, Lin Xiao can easily use this form to transform the formula that stumped him before into this form, and then into the module form, thereby achieving his goal.

"Well, let's call this form...submodular form for now."

"As for what other functions this submodular form has, we will talk about it later. Now, this string theory is more important."

Lin Xiao's eyes narrowed slightly, and then he turned his attention to his current research again, and then began to use this new module form to connect it to a basic formula of quantum mechanics.

That is, the Schrödinger equation.

The full name of Schrödinger equation is Schrödinger wave equation, which can describe the motion of microscopic particles. For each microscopic system, there is a corresponding Schrödinger equation. By solving this equation, you can know the wave function and corresponding energy of this microscopic system.

Now, Lin Xiao wants to use the Schrödinger equation to describe the particle motion during the diffraction and interference processes, and then connect the particle nature and wave nature.

As he calculated, the results appeared.

After solving the Schrödinger equation, it is clear that there is an unknown quantity, which causes the interference and diffraction of waves due to an effect that is probably vibration.

And as long as the algebraic expression representing the string is substituted into this unknown number, the entire formula can become perfect and harmonious.

"Sure enough, it's really the strings that work."

Lin Xiao was slightly amazed in his heart.

Who would have thought that in the interaction between waves, strings are the fundamental factor that leads to their interaction.

However, if you reproduce the process in your mind, the result is very reasonable.

If there is no one acting on it, there will be no interference and diffraction between waves, that is, coherent superposition of waves.

"Okay, now it's time to discuss how to use string theory to calculate the laws of coherent superposition of waves."

And the answer is already in sight.

"Set point p, the wave disturbance at point p can be approximated as..."

【ψ(r)≈-(iψ/2λ)(e^ik)……≈ψe^(ikr)/r】

"Suppose the string ξ also exists at point p. When a wave disturbance occurs, it will cause..."

"So, we can get the following system of partial differential equations..."

Finally, Lin Xiao combined two partial differential equations and wrote a system of partial differential equations. This system of equations revealed all the effects produced during the coherent superposition of waves.

Now, as long as he knows the source, wavelength or frequency of the wave, and knows where it is expected to interfere or diffract, he can easily calculate all the subsequent interference and diffraction processes of this wave.

And no matter how many beams there are, this system of equations can easily describe it.

Just like the Navier-Stokes equation, it is a system of equations that describes the conservation of momentum in viscous incompressible fluids.

Looking at this thing, Lin Xiao nodded with satisfaction.

The system's sound also sounded at this time.

"Congratulations to the host, you have completed the analysis of the secret of coherent superposition of waves, and at the same time created a new mathematical form such as the submodular form in the process. Your achievements in physics and mathematics can already be called outstanding. This reward : 2000 physics experience, 2000 mathematics experience, 80 truth points.”

Lin Xiao was even more happy when he heard the sound of the system.

The two subjects added up to 4,000 experience points, and the 80 truth points made him feel even more happy.

"Open personal panel."

He muttered silently in his mind, and his current situation emerged in his mind.

[Host: Lin Xiao]

[Truth point: 380]

[Cosmic Truth Branch Level]

[Mathematics: Level 5 (2100/10000)]

[Chemistry: Level 1 (2/50]

[Physics: Level 5 (2000/10000)]

[Biology: Level 1 (2/50)]

[Materials Science: Level 3 (560/1000)]

[Informatics: Level 1 (25/50)]

"Hmm...it seems a bit biased?"

Looking at the current levels of various subjects, Lin Xiao sighed inwardly. Mathematics and Physics were already at Level 5, but three were still at Level 1.

"Let's improve other levels when we have the opportunity in the future."

Without thinking any more, he exited the personal panel and continued to focus on the formula in front of him.

"So, this thing should be named... Lin's wave coherent superposition equations?"

After thinking about it in his mind, he couldn't help but smile on his face. Under the theory of naming it after Lin, he added another important person!

The importance of this new equation may not be as important as the Navier-Stokes equation. After all, the Navier-Stokes equation is used in the study of fluid mechanics, and the place where fluid mechanics is studied is far better than it is now. There is more research on this thing.

However, in terms of physical significance, this new partial differential equation can reveal a role of strings.

This is indirect proof of the existence of strings.

So you can imagine what kind of shock it will bring when this is known to the physics community.

Proving the existence of strings is a very difficult matter. According to past calculations by physicists, a particle collider at least as big as the Earth would be needed to smash the strings.

There are also indirect methods of proof. As Lin Xiao and Professor Edward Witten said before, when heavy ions collide, a closed string will be produced according to calculations, and the emergence of the closed string will cause a part of the energy to dissipate, but This kind of calculation still has greater requirements on experimental data.

But Lin Xiao's current method of indirect proof is quite simple.

It is known that coherent superposition occurs between waves. According to his proof of Lin's wave coherent superposition equation, it is pointed out that strings play a role in it. If strings do not play a role, it means that what string theory calculates is not strings. , but something else, but obviously what string theory calculates is a string, so there are strings.

This is such a logic. Of course, Lin Xiao doesn't care whether the physics community will approve it. The inverse sine theory physicists will definitely approve it, because they are already very eager for anything that can prove the existence of strings, and Physicists who don't like string theory will probably deny it because they will think that such a proof is not rigorous, and they will probably be more inclined to use particle colliders to conduct research.

Of course, these things are not considered by Lin Xiao.

Let the string theory physicists and other physicists argue.

Of course, we have to wait until he sends out the paper first.

However, he didn't have time to sort out papers for the time being.

In fact, this paper may not even need to be published.

After all, there are many places where wave diffraction and interference can be used, even in military applications, such as the stealth coating of fighter jets.

Stealth coating is a kind of absorbing material. The absorbing material mainly uses resistance, dielectric, and magnetic loss to absorb radar electromagnetic waves. How to absorb these electromagnetic waves with greater efficiency will test the internal molecules of the coating material. structure, and using this system of equations can solve this problem very well. When electromagnetic waves are irradiated into the absorbing coating material, the special structure inside is used to interfere and diffract these electromagnetic waves, allowing them to fall into the internal structure of the material. In the "microwave darkroom", it is eventually completely absorbed, thereby enhancing the effect of the invisible coating.

In addition to this function, the interference and diffraction of waves can also be used in many places, such as ultra-high precision sensors, such as the laser interferometer that was often used before, which utilizes the principle of interference, and if there is With Lin Xiao's formula, the level of precision can be improved again.

Another example is holographic projection technology, which uses the principles of interference and diffraction to record and reproduce the true three-dimensional image of an object.

The application of many of these technologies in the military may prevent Lin Xiao's formula from being published.

Therefore, Lin Xiao will also consider whether to release it based on the situation in the future.

Of course, for Lin Xiao, these things have to wait until he solves the problem at hand before talking about it.

After all, he now has to calculate what kind of crystal structure can amplify and reduce X-rays based on this equation that can describe interference and diffraction.

This is the purpose of spending so much time studying this thing.

For this problem, we need to understand why X-rays can be diffracted in the crystal structure. Of course, just study the principle of the X-ray diffractometer directly.