From Almighty Scholar to Chief Scientist

Chapter 251 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 describing the de Broglie wave, the so-called matter wave, which refers to the probability that matter may appear at a certain point and moment in space. Of course, this [matter] often refers to microscopic objects, not to say A person may appear in another place anytime and anywhere.

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

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

Of course, this connection is not close, only a few unknowns are connected, but when he substituted string theory into it, he did not have such expectations, because he felt that such Found it a bit too simplistic.

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

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

If this inference is put on arxiv, I am afraid it will 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 direction of algebraic geometry.

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

"How to convert this function to the modular form?"

After thinking for a moment, a sudden movement occurred in his mind.

He thought of something he had proposed.

Lin guessed.

Lin's conjecture states that any function can be transformed into a layer form.

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

Just like what Professor Deligne thought at the beginning, it will 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 a modular form.

Of course, this is really a bit of a sledgehammer.

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

"However, if it is in the form of a model..."

Lin Xiao fell into thinking again.

This problem must be solved. If it is not solved, he cannot verify the relationship between string theory and wave diffraction and interference.

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

Obviously, this is somewhat difficult.

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

In any case, what Lin Xiao likes to study the most is this kind of theoretical problem.

Applied science research requires running around and doing various experiments. He looks 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's his own style of painting. He holds a pen and faces complex mathematical formulas on a piece of paper. That's the style he thinks he should have.

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

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

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

"Through a special transformation of the original function, a new form can be created, and the new form can be multiplied by a simple matrix to obtain the modular form of the original function, um...seems like an accident, Made it a little complicated?"

Lin Xiao looked at the formula in his hand, and the various physical quantities in it, in his eyes at this moment, these are things that represent complex mathematical relationships.

However, in order to solve his problem, he still made a big fuss a little bit, 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, which is probably equivalent to the accompanying one, and can be transformed into the modular form after a simple transformation. However, its function is not limited to this, but its role in Relationships 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 modular form, and then achieve his goal.

"Well, let's name this form... the submode form for the time being."

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

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

That is, the Schrödinger equation.

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

Now, Lin Xiao is going to use the Schrödinger equation to describe the particle motion in the process of diffraction and interference, and then connect the particle and wave properties.

As he calculated, the result appeared.

After solving the Schrödinger equation, it can be clearly determined that there is an unknown, because of an effect that is probably vibration, which causes the interference and diffraction of waves.

And as long as the algebraic formula representing the string is substituted into this unknown, the whole formula can be made perfect and harmonious.

"Sure enough, the string is really working."

Lin Xiao was slightly amazed in his heart.

Who would have thought that in the negotiation between waves, the string is the fundamental factor leading to their negotiation.

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, the coherent superposition of waves.

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

And the answer is already in front of you.

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

【ψ(r)≈-(iψ/2λ)(e^ik)……≈ψe^(ikr)/r】

"Assuming that the chord ξ also exists at the point p when a wave perturbation occurs, which causes..."

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

In the end, Lin Xiao combined two partial differential equations and wrote down a system of partial differential equations, which revealed all the effects of the coherent superposition of waves.

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

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

Just like the Navier-Stokes equations, it is a system of equations describing the conservation of momentum of a viscous incompressible fluid.

Looking at this thing, Lin Xiao nodded with satisfaction.

And the sound of the system also sounded at this moment.

"Congratulations to the host, you have completed the analysis of the secret of the 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 excellence. This reward : 2000 physics experience, 2000 math experience, 80 truth points."

Hearing the sound of the system, Lin Xiao was even more happy.

There are 4000 experience points in the two subjects combined, and the 80 truth points make him feel very happy.

"Open personal panel."

He muttered silently in his heart, and his current situation appeared in his mind.

[Host: Lin Xiao]

[Truth points: 380]

【Universal truth branch level】

【Mathematics: Level 5 (2100/10000)】

[Chemistry: Level 1 (2/50)

【Physics: Level 5 (2000/10000)】

【Biology: Level 1 (2/50)】

[Materials: Level 3 (560/1000)]

[Informatics: Level 1 (25/50)]

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

Looking at the current grades of various subjects, Lin Xiao sighed in his heart. Mathematics and physics are already at the fifth level, but three of them are still at the first level.

"I'll upgrade to another level when I have a chance in the future."

Without thinking about it, 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 heart, he couldn't help but smile, and under the theory of naming it after Lin, he added another important member!
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 more than he is now. There are more things to study.

However, from a physical point of view, behind this new partial differential equation, it can reveal an effect of strings.

This is an indirect proof of the existence of strings.

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

It is very difficult to prove the existence of strings. According to the calculations of physicists in the past, a particle collider at least as large as the earth is needed to smash the strings.

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

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

It is known that there will be coherent superposition between waves, and according to his proof of Lin’s wave coherent superposition equation, it is indicated that strings are acting in it. If strings are not acting, it means that what string theory calculates is not strings , but another thing, but obviously the thing calculated by string theory is a string, so there is a string.

This is such a logic. Of course, Lin Xiao doesn’t care whether the physics community will recognize it. Anyway, string theory physicists will definitely recognize it, because they are already very eager for anything that can prove the existence of strings, and Those 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 for research.

Of course, these things are not in Lin Xiao's consideration.

Let the string physicists argue with other physicists.

Of course, we have to wait for him to send out the paper first.

However, he has no free time for sorting out papers.

Even, maybe this paper does not need to be published.

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

Invisible coating is a kind of wave-absorbing material. The wave-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 equation can solve this problem very well. When electromagnetic waves are irradiated into the absorbing coating material, and then use the special structure inside to realize the interference and diffraction of these electromagnetic waves, let them fall into the internal composition of the material. In the "microwave anechoic chamber", it is finally completely absorbed, which in turn improves the effect of the invisible coating.

In addition to this effect, the interference and diffraction effects on waves can also be used in many places, such as ultra-high-precision sensors, such as the laser interferometers that are often used before, which use 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 real three-dimensional image of an object.

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

So Lin Xiao will also consider whether to release it according to the situation in the future.

Of course, for Lin Xiao, these things have to wait for him to solve the problem before him.

After all, he still needs to calculate what kind of crystal structure can achieve the magnification and reduction of X-rays based on this equation that can describe interference and diffraction.

This is why he spent so much time researching this thing.

As for this question, it is necessary to understand why X-rays can be diffracted in the crystal structure. Of course, it is enough to directly study the principle of X-ray diffractometer.

(End of this chapter)