Chapter 457 The clown is actually me?
"."
Near a data terminal.
Looking at Xu Yun who confidently said the word 'intentional'.
A big question mark suddenly appeared on Suzuki Atsushi's face.
Is this unlucky kid acting out of common sense?
But soon.
Suzuki Atsushi recovered from his surprise, laughed angrily, and stared at Xu Yun:
"On purpose?"
"Xu Sang, that means you don't use the complete spectrum, and you deliberately do the eigenvector square root of the operator?"
Xu Yun nodded:
"That's right."
Suzuki Atsushi rolled his eyes silently. He originally thought that Neon Man's remarks when he discharged nuclear wastewater were shameless enough, but he didn't expect to meet someone with a thicker skin today:
"Why? Just because you want to show off your skills?"
Hear this.
Zhou Shaoping's expression on the other side of Suzuki Atsushi suddenly changed, and he subconsciously prepared to interrupt.
After all, if Xu Yun is allowed to continue talking, he will not be able to keep it even if he wants to when the responsibility is finalized.
Atsushi Suzuki, this old guy, has really sinister intentions.
However, before he could say anything, Zhou Shaoping felt someone tugging on his clothes.
He turned his head and found that Mr. Yang had arrived at a blind spot beside him at some point.
After meeting Zhou Shaoping's gaze, Mr. Yang glanced at him in a low voice:
"Xiao Zhou, let Xiao Xu continue."
Zhou Shaoping frowned when he heard this, and a trace of anxiety appeared on his face:
"But Mr. Yang, Xiao Xu will have no room for explanation at all"
Before Zhou Shaoping finished speaking, he saw Mr. Yang waving his hand towards him again, interrupting the second half of his words.
After a while.
Perhaps because he was worried about the confusion of Zhou Shaoping's authorities, Mr. Yang hesitated for a moment and added faintly:
"Xiao Zhou, how do you know"
"The data calculated by Xiao Xu must be wrong?"
Zhou Shaoping was stunned for a moment, and subconsciously wanted to retort, 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 ultimate figures like Higgs.
Even the most popular person is a quasi-Nobel Prize winner like Atsushi Suzuki.
As a result, 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, what follows is the rational thinking of a scientific researcher.
True.
Judging from the current magnitude between the enemy and ourselves, the Academy of Sciences group is undoubtedly an absolute minority.
But if analyzed theoretically.
Suddenly.
Zhou Shaoping's eyes became a little misty.
He thought of a possibility, the only possibility that fit the current situation.
But the probability of that happening is really too low.
And Zhou Shaoping's thinking also happened to eliminate the possibility of stopping Xu Yun.
Xu Yun pondered for a moment and shook his head at Suzuki Atsushi:
"Show off my skills? Mr. Suzuki, you misunderstood. How could I show off my skills on such an occasion?"
"It's just that during the previous calculation process, I discovered a somewhat serious problem."
"It is precisely because of this problem that I will choose another idea."
"What's the problem?"
"The pseudo-vector value of a finite-angle vector rotation within a certain range does not comply with the superposition commutative law."
"Pfft——"
Hearing Xu Yun's explanation, Atsushi Suzuki finally couldn't help laughing, as happy as Kennedy sitting in a convertible:
"Xu Sang, do you know what you are talking about? It does not comply with the law of superposition commutation?"
"The accuracy of vector connection of limited-angle vector rotation has been tested for decades. Any current particle, even the Pangea dark matter discovered by the Chinese Academy of Sciences, conformed to the corresponding model in the experiment just now."
"I do not deny that in some situations, the matrix elements of the rotation operator about the limited axis will indeed be more refined."
"But this kind of refinement is meaningless, not to mention that there are still many unresolved links in it. It is a real way to cause problems."
Hear this.
Many scholars around him nodded.
As Atsushi Suzuki said.
In current research in the physics community, limited-angle vector rotation is a common method of constructing bases, and the fit covers all known particles.
It's simple and reliable, and it never goes wrong.
The matrix element of the rotation operator around the limited axis is indeed higher in accuracy, but this so-called accuracy does not mean much.
What's more.
The perturbative basis constructed by the matrix element of the rotation operator around a limited axis is still far from being thoroughly studied in the physics community.
Because the concept of total angular momentum is too broad.
Friends who have studied mechanics all know this.
Angular momentum is one of the three conserved quantities in classical mechanics.
But if you ask again why angular momentum is conserved, I guess fewer people will know.
Actually.
The reason why angular momentum is conserved 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 trace 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.
By calculating the spinor field, we can find 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 spinor field corresponding to the particle.
In the particle stationary system, calculating the eigenvalue of the J operator shows that the eigenvalue is ±1/2.
This means that the spin of the particle corresponding to the spinor field is 1/2.
Since the spinor field must adopt the anti-commutative relationship when quantizing it, the spin 1/2 particles corresponding to the spinor field satisfy Fermi-Dirac statistics, so those particles are also called fermions - yes , which is why the fermion spin is semi-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.
Same reason.
The angular momentum of the vector field is also calculated, which also includes the spin term, and the particle with spin 1 corresponding to the vector field can be obtained.
Among the 61 kinds of elementary particles, 12 kinds of particles that transmit interactions are such spin 1 particles.
It includes photons that transmit electromagnetic interactions, eight types of gluons that transmit strong interactions, and two W particles and one Z particle that transmit weak interactions. 1+8+3=12.
Calculation of the scalar field will reveal that it has no spin and corresponds to a spin-0 particle. The Higgs particle, the last particle discovered among the 61 fundamental particles, is such a particle.
You see.
All current basic particles have a direct mathematical relationship with the angular momentum operator.
In the words of Zhong21.
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 previously the idea of treating the field quantity as a wave function rather than a coordinate operator.
Don't just say a word about this idea.
In fact, when it is completely summarized as a mechanism, it is at least a paper at the level of the main journal of Science.
Let’s take another example.
There is a limit to the amount of water a person can drink in one breath. Even if he is extremely thirsty, two bottles of 500 ml mineral water are almost enough.
Vector rotation with a limited angle is equivalent to such mineral water.
The matrix element of the rotation operator around the limited axis is a 10-liter bucket.
The capacity of a 10-liter bucket is obviously larger than that of a mineral water bottle, but for a single person's drinking volume, the large capacity of the bucket is actually meaningless.
On the contrary, because of its large volume and heavy weight, carrying the bucket consumes more energy than mineral water.
Therefore, compared with vector rotation with limited angles, the matrix element of the rotation operator around a limited axis is extremely cost-effective.
Then Suzuki Atsushi took a deep breath, suppressed the ecstasy in his heart, and pretended to be curious:
"Oh? The pseudovector values in a certain range do not comply with the superposition commutative law?"
"In that case, Xu Sang, can you find out the scope of the problem?"
Suzuki Atsushi's purpose was just to push Xu Yun to a point of no return. Unexpectedly, Xu Yun actually nodded happily:
"No problem. When TK is greater than 6, the constraint is greater than 7Φ, and the completely antisymmetric tensor is non-zero, what you get will be a massive vector field with a spin of 1/2 instead of 1, and the Lagrangian is in the form There will be an extra negative sign.”
Suzuki Atsushi was stunned for a moment, and had a subconscious reaction in his mind:
Is this guy bluffing?
With such intensive calculations, can he still find the specific interval?
How is this possible?
Anton Salinger, who was next to Suzuki Atsushi, reacted faster. He stepped over to the data terminal and compared the data seriously.
"TK is greater than 6 and the constraint is greater than 7K-G field. The completely antisymmetric tensor is non-zero"
Anton Salinger entered the data quickly, and after a few seconds, he frowned.
Although there is insufficient calculation time, the spin of the massive vector field mentioned by Xu Yun cannot be calculated for a while.
But for him, a top quantum physics expert in the world, the form of the Lagrangian is not difficult to judge.
Based on simple analysis, he can roughly judge the form of the Lagrangian.
There is indeed an extra minus sign.
This minus sign is not a purely mathematical negative number, but refers to negative energy.
Actually.
There is nothing wrong with pure negative energy. There are some examples in theoretical situations where negative energy can be completely achieved.
For example, in the Casimir effect, the suction force that occurs when two uncharged metal plates are very close to each other 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 we are constructing now is a vector field. Regarding the concept of vector field, there is a slightly formal saying in particle physics to describe it, called:
Energy is not limited to the lower world. E has a lower world but no upper world.
That is to say, the vector field situation with negative energy is not necessarily wrong, but it needs to be corrected, for example, by translating the field to obtain a point with lower potential energy, so as to obtain the true dynamic field equation, etc.
That is to say, this is a field that needs to be optimized.
More importantly.
In the calculation process of KG field, if you want the energy to be negative, there is only one situation:
The space vector part is 0, leaving only the time component.
This way.
It will also cause problems with the E-L equation and Hamiltonian density, and the Lorentz invariance will also be affected, eventually causing problems with the entire framework.
In other words.
In the situation mentioned by Xu Yun, there is indeed a possibility that the pseudovector value does not comply with the superposition commutative law.
Of course.
To be truly confident, further calculations are needed.
Think of this.
Anton Salinger couldn't help but turn his head and look at Xu Yun, re-examined his nominal "disciple", and then said to Tehuft who rushed to his side again:
"Gerald, you have the best math skills among us, please excuse me."
Without further words, Tehuft understood what he was thinking:
"OK, leave it to me."
Finished.
The big man with a huge bald spot on his forehead picked up his pen and started doing calculations quickly.
The spin of the mass vector field belongs to the category of quantized calculations, and the core is the plane wave solution of the E-L equation.
Then, by verifying that the z-axis is parallel to the direction of momentum, the completeness relationship is established. By adopting commutative quantization conditions for the three polarization vectors, the spin of the mass vector field can be easily calculated.
Swish Swish Swish——
Because the data was complete, Tehuft's calculations were quick.
It only took a few minutes.
He paused with his pen, raised his head and gave Anton Salinger a look of unknown meaning, then turned to Witten and said:
"Edward, Xu's statement is correct. According to our thinking, the vector field spin is calculated to be 1/2."
"."
In an instant, you could hear needles dropping all around you.
The cameraman at the scene cleverly zoomed in and captured the expressions of each boss at this time.
Surprised,
Confused,
Question,
Anger,
At this time, different expressions appeared on the faces of scholars from different camps.
It was said dozens of lines above.
Currently, there are only three types of elementary particle fields discovered in physics: scalar field, spinor field, and vector field, all of which satisfy Lorentz symmetry.
The spinor field corresponds to particles with spin 1/2, which are 48 types of fermions.
The vector field corresponds to particles with spin 1, that is, 12 types of bosons.
In other words, the spin value of the vector field that can be described must be 1, and it can never be 1/2.
Still taking the Qidian boutique badge mentioned before as an example.
The average subscription requirement for premium badges is 3,000 average subscriptions, that is, only books with an average subscription of 3,000 or more can enter the premium library.
In other words.
A book with 400 subscriptions cannot have a high-quality badge, nor can it be retrieved by the high-quality library.
A high-quality product is equal to or greater than 3,000 uniformly, otherwise it is a non-high-quality product. This is an iron law - not only an iron law of the database, but also a concept that exists in the reader's cognition.
What Tehuft discovered at this time was equivalent to finding a novel with an average subscription of 400 in a boutique channel.
In this case, there is either an eye problem.
Either
An error occurred in the framework program for indexing books.
This situation combined with the current reality is.
Including Witten, the frameworks calculated by the other eight groups are not consistent with the characteristics of Pluto particles.
It’s not just Tehuft who realizes this, but also David Gross and Nima.
and
Atsushi Suzuki.
Gulu——
The top boss from Neon swallowed hard, and from the corner of his eye, he saw several cameras turning their lenses towards him.
Although there was no physical attack, he truly experienced what it meant to have a light on his back.
All the ridicule he had directed at Xu Yun before was now harshly reflected back on him.
clown
It's me?
impossible!
Absolutely impossible!
A row of fine beads of sweat instantly appeared on Suzuki Atsushi's forehead. The old Baga, who looked as if he could belch at any time, began to think rapidly.
A few seconds passed.
He suddenly thought of something, and the decibel level of his voice increased a lot:
"Wait! Mathematics is mathematics after all. Maybe the particles still obey the vector rotation base of limited angles on the physical level - there is precedent for this situation."
"For example, this is the case with the four-dimensional line element of mass in electrodynamics. After introducing certain variations, it still conforms to the mathematical formula. Who can guarantee that the particles will not be like this?"
Suzuki Atsushi's words aroused the approval of many people at the scene.
Some of these people do not want to lose face like this and are not willing to admit failure in a scrupulous manner.
Some people simply agree with Suzuki Atsushi's statement.
After all, the development histories of the two disciplines of mathematics and physics are, in some sense, their respective histories of optimization and self-consistency.
Even in 2023, many physical phenomena still cannot be completely answered by mathematics, such as quantum collapse.
Just like what was said before.
Any physical phenomenon must eventually be described and explained using mathematics, but the node of this "explanation" may be very long.
Probably decades ago.
Maybe decades from now.
It could be today.
Or maybe the next chapter. Ahem, tomorrow.
So putting aside political overtones and character, what Suzuki Atsushi said does have some truth to it.
Based on the current level of human mathematical development, pure mathematics cannot yet determine everything.
It is often the norm to first discover anomalies and then optimize and introduce them.
See this situation.
Witten couldn't help but glance at Atsushi Suzuki:
"So Mr. Suzuki, what do you mean"
Suzuki Atsushi 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 particles under the two frameworks, and then"
"Look at which energy level you can capture that particle!" (End of Chapter)