Into Unscientific

"."

Near the data terminal.

Looking at Xu Yun who confidently said the word "intentional".

A big question mark suddenly appeared on Suzuki Atsuto's face.

This unlucky kid didn't play cards according to common sense?

But soon.

Atsuto Suzuki recovered from his astonishment, laughed angrily, and fixed his eyes on Xu Yun:

"on purpose?"

"Xu Sang, that is to say, you don't need the complete spectrum, but you purposely do the eigenvector extraction of the operator?"

Xu Yun nodded:

"That's right."

Atsuto Suzuki rolled his eyes silently. He thought that Neon Man's remarks when he discharged nuclear waste water were shameless enough, but he didn't expect to meet a thick-skinned one today:

"Why? Just because you want to show off your skills?"

I heard this.

Zhou Shaoping, who was on the other side of Atsuto Suzuki, suddenly changed his expression, and subconsciously prepared to interject.

After all, if Xu Yun is allowed to continue talking, then after the responsibility is finalized, he may not be able to keep it.

Atsuto Suzuki, the old Baga, really has sinister intentions.

But before he could say anything, Zhou Shaoping felt someone pulling his clothes.

He turned his head and found that Mr. Yang had arrived at a certain blind spot of the camera around him at some point.

After looking at Shaoping last week, Mr. Yang gave him a look in a low voice:

"Xiao Zhou, let Xiao Xu continue."

Zhou Shaoping frowned when he heard this, with a hint of anxiety on his face:

"But Mr. Yang, Xiao Xu has absolutely no room for explanation in this way."

Zhou Shaoping didn't finish his sentence, but saw Yang Lao waved his hand at him again, interrupting the second half of his speech.

After a while.

Perhaps because he was worried that Zhou Shaoping's authorities would be fans, Mr. Yang hesitated for a while, and added:

"Xiao Zhou, how do you know?"

"The data calculated by Xiao Xu must be wrong?"

Zhou Shaoping was taken aback for a moment, and subconsciously wanted to refute, isn't this obvious?

After all, the leaders of the other eight groups are either Nobel laureates or uncrowned kings like Witten, and there are also some extremely powerful figures like Higgs.

Even the most stretched things are quasi-Nobel Prize winners like Atsuto Suzuki.

In the end, you said that Xu Yun's answer was correct, but the other eight teams were wrong?

How is this possible?

But after the emergence of perceptual thinking, the rational thinking of a scientific researcher followed.

Indeed.

Judging from the current magnitude between the enemy and ourselves, the Academy of Sciences group is undoubtedly an absolute minority.

But if it is analyzed theoretically.

Suddenly.

Zhou Shaoping's gaze became a little misty.

He thought of a possibility, the only possibility that fit the current situation.

But the chances of that happening are really, really low.

And Zhou Shaoping's thinking like this just happened to cut off his possibility of stopping Xu Yun.

Xu Yun pondered for a moment, then shook his head at Atsuto Suzuki:

"Show off skills? Mr. Suzuki, you misunderstood, how could I show off skills on such an occasion?"

"It's just that during the previous calculation process, I discovered a somewhat serious problem."

"It was prompted by this question that I chose another way of thinking."

"what is the problem?"

"The vector rotation of a finite angle is a pseudo-vector value in a certain range, which does not conform to the law of superposition commutation."

"Pfft—"

Hearing Xu Yun's explanation, Atsuto Suzuki finally couldn't help laughing, as happy as Kennedy in a convertible:

"Xu Sang, do you know what you're talking about? Doesn't conform to the law of superposition and exchange?"

"The accuracy of the vector rotation of the limited angle in terms of vector connection has been tested for decades. Any particle at present. Even the Pangu dark matter discovered by the Chinese Academy of Sciences, also conforms to the corresponding model in the experiment just now."

"I don't deny that in some cases, the matrix elements of the rotation operator around the defined axis will indeed be finer."

"But this kind of refinement is meaningless, not to mention that there are still many unsolved links in it, and it is a method that may really cause problems."

I heard this.

Many scholars around nodded.

As Atsuto Suzuki said.

In the current research in the physics community, vector rotation with limited angles is a common base construction method, and the degree of fit covers all known particles.

It's clean and reliable, and there's never been a single error.

The matrix element of the rotation operator around the limited axis is indeed higher in precision, but this so-called precision is really meaningless.

more importantly.

At present, in the field of physics, the perturbation base constructed by the matrix elements of the rotation operator around the limited axis is far from being thoroughly studied.

Because the concept of full angular momentum is too broad.

Anyone who has studied mechanics knows this.

Angular momentum is one of the three conserved quantities in classical mechanics.

But if you ask why angular momentum is conserved, there are probably fewer people who know it.

Actually.

The reason for the conservation of angular momentum is simple:

The rotational symmetry of space is the real cause of the conservation of angular momentum, that is, each continuous symmetry corresponds to a conserved quantity.

So more strictly speaking.

is to define the conserved quantity corresponding to the rotational symmetry of space as angular momentum.

In other words.

As a micro-differential operator of a space rotation group, angular momentum can generate all space rotation transformations.

So different fields correspond to different angular momentum operators.

Take the spinor field as an example.

It can be found from the calculation of the spinor field that its angular momentum can be written in the form of J=L+σ/2.

where L is the orbital angular momentum, and σ/2 is called the spin of the particle corresponding to the spinor field.

In the static system of particles, the eigenvalue of the J operator can be calculated to find that the eigenvalue is ±1/2.

This means that the spinor field corresponds to 1/2 the spin of the particle.

Since the spinor field needs to adopt the anti-commutation relation when it is quantized, this makes the spin 1/2 particles corresponding to the spinor field satisfy Fermi-Dirac statistics, so those particles are also called fermions—that’s right , which is why the spin of fermions is half-odd.

Among the 61 kinds of elementary particles, 36 kinds of quarks and 12 kinds of leptons (including electrons and neutrinos) are such fermions, 36+12=48 kinds.

the same way.

The angular momentum of the vector field is also calculated, which also includes the spin item, and the particle corresponding to the vector field with a spin of 1 can be obtained.

Among the 61 kinds of elementary particles, 12 kinds of particles that transmit and interact are just such spin-1 particles.

Including photons that transmit electromagnetic interactions, 8 kinds of gluons that transmit strong interactions, and two W particles and one Z particle that transmit weak interactions. 1+8+3=12.

Calculations on the scalar field would reveal that it has no spin, corresponding to a spin-0 particle, one of the last of the 61 fundamental particles to be discovered—the Higgs particle is such a particle.

look.

All of the basic particles currently have a direct mathematical connection with the angular momentum operator.

In the words of middle school.

The matrix element of the rotation operator around the limited axis is the “mystery” that touches the “origin of the world”.

For example, Mr. Yang mentioned earlier the idea of ​​treating the field quantity as a wave function instead of a coordinate operator.

Don't look at this idea and just say a word.

In fact, after fully summarizing it into a mechanism, it is at least a paper at the level of the main journal of "Science".

Another example.

There is a limit to how much water a person can drink in one breath. Even when extremely thirsty, two bottles of 500ml mineral water are almost enough.

The vector rotation of limited angle is equivalent to such mineral water.

And the matrix element of the rotation operator around the limited axis is a 10-liter water bucket.

The volume of a 10-liter bucket is obviously larger than that of a mineral water bottle, but for a single drinking volume for a single person, the large volume of the bucket is actually meaningless.

On the contrary, because of its large volume and heavy weight, it takes more energy to carry the bucket than mineral water.

Therefore, compared with the vector rotation with limited angle, the cost performance of the matrix element of the rotation operator around the limited axis can be described as extremely low.

Then Atsuto Suzuki took a deep breath, suppressed the ecstasy in his heart, and put on an expression of inquiry and curiosity:

"Oh? Pseudovector values ​​in a certain range do not conform to the law of superposition commutation?"

"In this case, Xu Sang, can you find out the scope of the problem?"

Atsuto Suzuki's purpose was to force Xu Yun to the point where he could not retreat, but unexpectedly, Xu Yun nodded readily:

"No problem, when TK is greater than 6, the constraints are greater than 7Φ, and the total antisymmetric tensor is non-zero, the result will be a mass vector field with spin 1/2 instead of 1, and the Lagrangian is in the form There will be an extra minus sign."

Atsuto Suzuki was stunned for a moment, and there was a subconscious reaction in his mind:

This guy is bluffing, right?

With such an intensive calculation, can he still find a specific interval?

How can this be?

Anton Salinger, who was next to Atsuto Suzuki, reacted faster, stepped to the side of the data terminal, and carefully compared the data.

"TK is greater than 6 constraints are greater than 7K-G field. All antisymmetric tensors are not 0"

Anton Salinger quickly entered the data, and after a few seconds, he frowned.

Although there is not enough calculation time, the mass vector field spin that Xu Yun mentioned cannot be calculated for a while.

But for a top quantum physicist like him, the form of the Lagrange quantity is not difficult to judge.

According to a simple analysis, he can roughly judge the form of the Lagrange quantity.

There is indeed an extra minus sign.

This negative sign is not a negative number in pure mathematics, but refers to the negative energy.

Actually.

There is nothing wrong with purely negative energy. There are some examples in theoretical situations that can have negative energy.

For example, in the Casimir effect, when two uncharged metal plates come very close to each other, the suction force comes from the energy difference of the vacuum inside and outside the plates, and the vacuum between the plates has negative energy.

But the problem is that what is being constructed right now is a vector field. For the concept of a vector field, there is a slightly sophisticated saying in particle physics to describe it, which is called:

Energy is not limited to the lower bound, E has a lower bound, but no upper bound.

That is, the vector field situation with negative energy is not necessarily wrong, but it needs to be corrected, such as obtaining a point with lower potential energy through the translation field, so as to obtain the real dynamic field equation and so on.

That is, this is a field that needs to be optimized.

More critically.

In the calculation process of the KG field, if you want the energy to be negative, then there is only one situation:

The space vector part is 0, leaving only the time component.

Thus.

It will also lead to problems with the E-L equation and the Hamiltonian density, and the Lorentz invariance will also be affected, eventually causing problems with the entire framework.

In other words.

In the situation Xu Yun mentioned, there is a possibility that the pseudo-vector value does not conform to the law of superposition and commutation.

Of course.

If you want to really hit it, you need to do further calculations.

Think here.

Anton Salinger couldn't help turning his head to look at Xu Yun, re-examined his nominal "disciple", and said to Te Hooft who rushed to his side again:

"Gerald, you're the best at counting among us, sorry to trouble you."

Without further words, Te Hooft understood his thoughts:

"OK, leave it to me."

finished.

The big guy with a huge patch of baldness on his forehead picked up a pen and quickly started doing calculations.

The spin with mass vector field belongs to the category of quantization calculation, and the core is the plane wave solution of the E-L equation.

Then, the completeness relation is verified by making the z-axis parallel to the momentum direction, and the three polarization vectors adopt the condition of easy quantization, and the spin with mass vector field can be easily calculated.

Swish Swish Swish——

Since the data is complete, Te Hooft's calculations are very fast.

It was only a few minutes before and after.

He paused the pen tip, raised his head and gave Anton Salinger a look of unknown meaning, then turned his head to Witten and said:

"Edward, what Xu said is correct. According to our thinking, the spin of the vector field is calculated to be 1/2."

"."

In an instant, needles could be heard all around.

The cameraman at the scene cleverly zoomed in and captured the expressions of each big shot.

surprise,

Puzzled,

question,

anger,

At this time, different expressions appeared on the faces of scholars from different camps.

Dozens of lines above have said it.

At present, the fields of elementary particles discovered by the physics community are only scalar fields, spinor fields, and vector fields, all of which satisfy the Lorentz symmetry.

The spinor field corresponds to the spin 1/2 particles, that is, 48 ​​kinds of fermions.

The vector field corresponds to the particle with spin 1, that is, 12 kinds of bosons.

That is to say, the spin value of the vector field that can be described must be 1, and it can never be 1/2.

Still take the starting point boutique badge mentioned before as an example.

The average order requirement for the boutique badge is 3,000 average subscriptions, that is, only books with more than 3,000 average subscriptions can enter the boutique library.

In other words.

It is impossible for a book with 400 orders to have a boutique badge, and it is impossible to be retrieved by the boutique library.

A high-quality product is equal to or greater than three thousand, and vice versa is not a high-quality product. This is an iron law-not only the iron law of the database, but also a concept that exists in the reader's cognition.

At this time, what Te Hooft discovered was equivalent to finding a novel with 400 subscriptions in the boutique channel.

This is either a problem with the eyes.

either

An error occurred in the framework program for indexing books.

This situation combined with the current reality, that is.

Including Witten, the frameworks calculated by the other eight groups do not conform to the characteristics of Pluto particles.

It was not only Tehooft who realized this, but also David Gross and Nima.

as well as

Atsuto Suzuki.

Gollum—

The top boss from Neon swallowed heavily, and from the corner of his eye, he caught sight of several cameras turning their lenses on him.

Although there was no physical attack, he really experienced what it means to be like a man on his back.

All the ridicule he had directed at Xu Yun before, all of which were ruthlessly reflected on himself at this time.

clown

It was me?

impossible!

No way!

A row of fine beads of sweat instantly appeared on Suzuki Atsuto's forehead, and this old Baga, who looked as if he could burp at any time, started to spin his mind rapidly.

A few seconds passed.

He suddenly thought of something, and the decibels of his voice increased a lot:

"Wait! Mathematics is mathematics after all. Perhaps the particle still obeys the vector rotation basis of finite angle on the physical level-there is a precedent for this situation."

"For example, the four-dimensional line element of mass in electrodynamics is like this. After introducing some variations, it still conforms to the mathematical formula. Who can guarantee that the particle will not be like this?"

Atsuto Suzuki's remarks aroused the approval of many people at the scene.

Some of these people are unwilling to lose face like this, and are unwilling to admit defeat sloppily.

Some of them simply agree with Atsuto Suzuki's statement.

After all, the history of the development of the two disciplines of mathematics and physics, in a sense, is actually their own history of optimization and self-consistency.

Even in 2023, many physical phenomena, such as quantum collapse, still cannot be fully solved by mathematics.

As said before.

Any physical phenomenon must be described and explained by mathematics in the end, but the nodes of this "explanation" may be very long.

Probably decades ago.

It could be decades away.

Possibly today.

Or maybe the next chapter. Ahem, tomorrow.

So regardless of political color and character, what Suzuki Atsuto said does have some truth.

At the current level of human mathematics development, pure mathematics is not yet able to determine everything.

It is often the norm to find the abnormality first, and then optimize and introduce the abnormal point.

See this situation.

Wei Teng couldn't help but look at Atsuto Suzuki:

"So Mr. Suzuki, what do you mean"

Atsuto Suzuki glanced back at him, and waved his hand vigorously, as if to cheer himself up:

"The Fermi surface data of the Academy of Sciences group and our other eight groups are different, which means that the theoretical energy levels of the particles must also be different."

"So I think we can first determine the theoretical energy levels of the particles under the two frameworks, and then"

"Look at which energy level you can capture that particle!"