Hearing these four words coming out of Xu Yun's mouth, Zhao Zhongyao's eyebrows, which were already full of joy, were raised again very obviously.
Degenerate vacuum.
It is not difficult to see from the literal meaning that this concept can be discussed in two parts:
Degeneracy, and vacuum.
As we all know.
The word vacuum is somewhat similar to the second-level page, and it can also be divided into two third-level pages...that is, two scenarios:
One is the vacuum in macroscopic physics.
The second is microscopic... or vacuum in the quantum concept.
The former is easy to understand and refers to the space being empty or a person not wearing underwear.
But the vacuum in the quantum concept... is much more complicated.
The concept of quantum vacuum can be traced back to twenty years ago, around 1940.
At that time, the world war was in full swing, and the world of physics was developing quietly and rapidly under the flames of the war.
At that time, Dirac used the Dirac equation to establish a model of the hydrogen atom. The model consisted of a Coulomb potential that attracted each other between a proton and an electron.
Mentioned earlier.
The Dirac equation describes the behavior of fermions, of which protons and electrons are also two typical representatives.
The so-called typical naturally means that their research has been very in-depth and transparent.
Therefore, physicists also think that they can have a good understanding of the energy levels of hydrogen atoms through the Dirac equation. After all, the particles that make up it have no secrets.
At that time, the physicists in Milan were even opening champagne while cheering the emergence of a new model - the sum of three round things, protons, electrons, and hydrogen atoms, was three to zero. How could this be a loss?
until.....
A man from across the sea named Willis Lamb conducted an experiment at the University of Liverpool, which broke all the tranquility without warning.
1947.
When Lamb was doing research on the fine structure of hydrogen spectra, an abnormal result appeared in the experiment:
The hydrogen spectrum has a slight energy difference in the two quantum energy levels of 22S1/2 and 22P1/2.
According to the Dirac equation, the energies of these two quantum states should theoretically be the same.
However, the energy difference discovered by Lamb was approximately around 1028MHz, and after repeated confirmation, the possibility of experimental error was ruled out.
Lamb later named this difference the Lamb shift, and he won the 1955 Nobel Prize in Physics for this discovery.
The Lamb shift shows that the Dirac equation is not perfect under delicate conditions, and the subtle energy level difference implies that physicists still have some content to add.
And this content is...
Quantum vacuum—or vacuum fluctuations.
That is to say, there is not nothing within the scope of quantum vacuum, but there is an incalculable field...that is, energy.
It is a collection of different virtual and real particles that constantly appear and disappear. These extremely short-lived particles are not noticed in 99.99999% of cases, but in some cases vacuum forces may produce measurable effects.
For bosons, this energy is positive.
For fermions, this energy is negative.
That is, the quantum vacuum is empty but not empty. This is an important conclusion of quantum field theory. The so-called Casimir force is also a category of this part.
Of course.
The above is Xu Yun's understanding when he traveled through time...that is, in later generations in 2023. It is much deeper and clearer than it is today.
For example, later generations also defined another related concept called vacuum decay.
Its content is as follows:
Everything in the universe will spontaneously tend to the lowest energy state, similar to water flowing downwards.
Therefore, if the vacuum of the universe is not in the lowest energy state, then under certain conditions, the vacuum of the universe will "fall" to a lower energy state.
Assuming that the vacuum of the universe is not in the lowest energy state, then we can call it a "pseudo vacuum".
Corresponding to this is the cosmic vacuum in the lowest energy state, which can be called "real vacuum".
for example.
There is an iron ball halfway up a mountain.
Although it has a tendency to continue falling, it will not continue to fall due to a terrain obstruction halfway up the mountain.
But if you use a certain force to push the iron ball over the terrain blocking it, it will inevitably continue to fall.
Same reason.
If enough energy is injected into the pseudo vacuum.
Then the pseudo vacuum can break through the energy barrier and then fall toward the real vacuum, and vacuum decay occurs.
To know.
The energy released by vacuum decay is actually very, very large, enough to cause the surrounding pseudo-vacuum to break through the energy barrier.
in this case.
If vacuum decay occurs in a certain area of the universe, the energy released will cause vacuum decay in the surrounding space.
And the vacuum decay of the surrounding space will cause more spaces to also undergo vacuum decay, and the infinite matryoshka...
Eventually, this will form an unstoppable chain reaction, and the result will be a spherical space composed of "real vacuum" that rapidly expands in the universe.
And theoretically speaking.
The expansion speed of this spherical space is actually the speed of light.
At the same time, the "surface" of this spherical space is filled with huge energy.
Therefore, wherever it passes, many celestial bodies in the universe will fall apart, and physical constants will undergo huge changes.
See here.
Does any classmate feel that this description is familiar?
Does it feel like a black hole is similar to this?
Unfortunately, you are already familiar with it - black holes are not actually a model of vacuum decay.
but......
The finale of a certain fisherman's next book has something to do with vacuum decay.... (Yes, I have already thought about the finale of the next book. It can be regarded as an easter egg that spans a book. I'm being pretentious. I hope it will be published.
I can still see you at the end of this book)
This chapter is not finished yet, please click on the next page to continue reading the exciting content! Okay.
His eyes returned to reality.
Except for the vacuum.
Another concept of degeneracy is relatively simple.
The eigenvalue of a Hermitian operator has multiple eigenstates, which is degeneracy.
For example, the hydrogen atom orbit mentioned above has two degeneracies: angular momentum and spin.
Give another example.
Students who have read online novels should all know this.
An online writer may have several books under his pen name.
Although these books have different grades, word count, and content, they are all created by the same author on the same website. These books are the degeneracy of pseudonyms.
Therefore, degenerate vacuum refers to the vacuum prototype of an eigenstate, that is, another state transformed when the vacuum is non-invariant to the system group G.
This state undergoes transformation from the columnar symmetry ground state, ultimately leading to the emergence of the scalar boson.
If you still can’t understand the above sentence, let’s still take online novels as an example:
He is also a writer called Thirty Thousand Fishing Guys Every Day. He has two books under this pen name:
A book called "Handbook of Conquest of Different Worlds".
The other book is called "The Empire of Technology Begins by Eliminating Cockroaches".
The protagonist of the former book is called Wu Fan, and the protagonist of the latter book is called Donkey.
When you talk about the vacuum state of "Handbook of Conquest of Different Worlds", the characters that come to mind must be Wu Fan, Cao Yi, Lin Ziming...that is, the gauge boson with a vector.
And if you are talking about the degenerate vacuum of "The Empire of Technology Begins with Cockroaches", then the characters discussed will naturally become scalar bosons such as donkey, axe, and Lao Su.
That is, the role correspondence book = gauge/scalar boson corresponding to their respective degenerate states.
As for the different characters in the book, they are different types of gauge bosons, such as photons and gluons, etc.
"..."
Then Zhao Zhongyao was silent for a while, picked up the ballpoint pen and turned it around in his hand for a while, and said to Xu Yun:
"Xiao Han, I have a question... If a degenerate vacuum is established, what will its system look like?"
"After all, degenerate vacuum is just a state, and the principle supporting the existence of this model is the real core."
"Just like we said that after the invention of the perpetual motion machine, it can travel across the stars. Compared with the subsequent behavior, how to come up with the design model of the perpetual motion machine is the key - for the existing framework system, the perpetual motion machine is simply not a problem.
Things that might happen.”
Xu Yun smiled understandingly when he heard this. Naturally, he knew this truth very well:
"Director Zhao, you are right. Compared with the degenerate vacuum model, deeper principles are obviously the key."
"As for this principle... Director Zhao, have you ever heard of spontaneous symmetry breaking?"
"Spontaneous symmetry breaking?"
Zhao Zhongyao blinked and quickly thought of something:
"Is it the theory of superconductivity? It seems that the properties of matter suddenly change from a symmetrical state to an asymmetrical state spontaneously?"
Xu Yun nodded vigorously:
"That's right."
Spontaneous symmetry breaking.
Its English name is Spontaneous symmetry breaking, and its abbreviation is the somewhat subtle SSB.
This is a very common phenomenon in physics. Its mathematical principle is based on the gauge theory of the continuous group SU(2). The concept was jointly proposed by Yang Lao and Mills 7 years ago.
This concept is actually quite easy to understand. Have you all eaten or seen Yanjing’s copper hot pot?
Assuming that a small ball is stationary on the top of a copper hot pot, then the small ball must be unstable and will fall into the pot along the core of the furnace when disturbed.
before the ball falls.
Any position in a circle of the copper pot is equal, and the system has rotational invariance, that is, it is the same and symmetrical no matter how it is rotated.
but......
Things will be different when the ball falls.
The ball will eventually only stabilize at a certain position. At this time, the system, including the ball, no longer has rotational invariance.
This is a spontaneous symmetry breaking - the ball falling is "spontaneous", and the lack of rotational invariance is breaking.
Zhao Zhongyao was not unfamiliar with this concept, so he quickly made a guess:
"Spontaneous symmetry breaking...Xiao Han, could it be that there are terms in the pull-type density that obviously break some symmetry, such as the mass term of the Dirac field, thus destroying the conservative symmetry?"
Xu Yun:
"?!"
Then he didn't wait for Xu Yun to answer.
Zhao Zhongyao touched his chin again, picked up the pen and started calculating on the paper:
"I remember that the expression for superconductivity should be...if it is introduced into particle physics, it should be a spontaneous breaking of local symmetry."
"Considering particles in a one-dimensional space, then L=12(?μσ)2?12m2(σ)2..."
A few minutes later.
Zhao Zhongyao suddenly let out a sigh:
"...Hmm, isn't that right?"
"The stable vacuum state does not have cylindrical symmetry, so there are infinitely many degenerate ground states under transformation, or there is a non-zero mass field, right?"
After hearing Zhao Zhongyao's words, Lu Guangda, Zhu Hongyuan and others on the side couldn't help but quickly walked to him.
When Li Jue saw this, he glanced at the empty surroundings and followed suit.
"There really is a non-zero mass field..."
Hu Ning took the calculation paper and looked at the results for a while, and as always, he considered his own problems first:
"Old Zhao, could it be that you made a miscalculation?"
Zhao Zhongyao immediately shook his head, pointed at the calculation paper and explained:
"Impossible, not to mention how complicated the commutation process of Lie algebra structural constants is, please look here first."
"Look, this non-zero mass field has an independent supplementary term with root number 2 in front of it. This alone is enough to prove the existence of the non-zero field."
"Even if there is an error in my calculation, the error can only be in the specific expression of the non-zero field, not in its existence."
"Speaking of which, Lao Hu, you should change your pessimistic personality and become more confident. Why do you always doubt yourself first?"
This chapter is not over yet, please click on the next page to continue reading! Hu Ning shrugged and said nothing.
no way.
It's not that he is unconfident, it's just his character.
When he encounters an abnormality when solving problems or doing experiments, he will first consider whether there is something wrong with him. Only after eliminating his own fault will he be able to think about the next step.
This kind of mentality cannot be considered pessimistic. It should be said that it is somewhat stable?
Seeing that these big guys encountered another problem during the discussion, Xu Yun couldn't help but cough lightly and prepared to give a specific answer:
"Comrades, I have something to say, please listen carefully..."
As a result, before he finished speaking, Zhao Zhongyao and others turned their heads at the same time and interrupted him:
"Xiao Han, hold your tongue! Let us think for ourselves!"
Lao Guo even handed Xu Yun a cattail leaf fan, with an obvious meaning - just stay where you need to cool off.
Xu Yun:
"?????"
It's like killing a donkey...
Then, under Xu Yun's confused expression, many big guys turned their heads again and discussed the issue again.
Lu Guangda pondered for a moment and then took the initiative to say:
"....Director Zhao, if it's not a calculation error, then it's a mistake in group theory."
"In that case... I have an idea. Can we manually add an obvious defect to deform the vacuum?"
Say it.
Lu Guangda also picked up the pen and drew a pattern on the paper again.
how to say......
Let’s take a not-so-elegant example.
The original image drawn by Zhao Zhongyao was a butt, with both left and right sides symmetrical, and the tips of the left and right buttocks were the lowest energy points.
The image drawn by Lu Guangda is "skewed" a lot, and the two sides are obviously not equal - the right side is obviously larger than the left side.
But soon.
Zhu Hongyuan shook his head and denied Lu Guangda's guess:
"Unlikely, Comrade Guangda, the artificial correction is still too obvious, and this discrete model should not be able to generate a continuous field."
Lu Guangda thought for a few seconds and nodded.
Too.
His idea has a very obvious optimization intention, and the behavior of the particles is obviously unlikely to be changed according to this idea.
It's like you want to buy a five million house, but you only have 20,000 yuan on your bank card.
As a result, you used P-picture software to change it to five million, which seems to be enough to buy a house, but in fact it is of no use at all.
Unless you are so lucky that there is a bug in the banking system when you transfer the money, there is no way this house will fall into your hands.
Not to mention that this discrete model really cannot deduce a continuous field. It is better to use Feynman's path integral quantization...
However, Lu Guangda was not discouraged. The spontaneous symmetry breaking was related to his good friend Yang Zhenning, so this boss seemed particularly active at this time.
I saw him staring at the calculation for a while, and then came up with an idea:
"Since manually adding obvious breaking terms does not work... then is it possible that the combination of gauge symmetry and spontaneous breaking caused this mass field to be 'eaten' by the zero-mass gauge field?"
"For example, the gauge symmetry of the electroweak interaction is SU(2)LxU(1). Only by introducing the Yukawa coupling without destroying the gauge symmetry of the Lagrangian quantity can the mass of the meson be consistent with the derivation."
This time.
Zhao Zhongyao and others no longer refuted Lu Guangda, but fell into deep thought at the same time.
Yukawa coupling.
It refers to yukawa coupling, proposed by Hideki Yukawa of Neon.
This person is one of the founders of modern neon physics and is an unignorable figure in the entire history of particle physics:
He was the first neon person to win the Nobel Prize. He proposed the famous Yukawa coupling and Yukawa coupling potential, and also predicted the existence of pions.
However, due to this person's right-wing political leanings, Xu Yun has always had a public dislike of this person, and would diss him once to write a book.
To what extent is this person right?
for example.
At the Nobel Prize Award Ceremony, he openly called a certain war a "war of loyalty" and said, "There are still newly established unstable regimes around Neon, and this unstable regime should be curbed for the sake of peace."
trend】.
By the way.
Yukawa Hideki said this on December 10, 1949, and it is self-evident who he refers to.
Compared with his contemporary Sakata Shoichi, who was a true pacifist and a friend of China, Yukawa Hideki was on a par with heaven and earth - even though Sakata Shoichi did not win the Nobel Prize in academics.
Later, Yukawa Hideki also became a toilet seat brand, and the manufacturer was still a domestic company in Pengcheng. This can be regarded as some kind of retribution...
Of course.
Just like Song Huizong was also a master of calligraphy.
No matter how bad Yukawa Hideki's character is, his academic achievements cannot be ignored.
For example, Lu Guangda's idea at this time did not introduce Yukawa coupling...or the meson concept really didn't work.
Because it is analyzed according to normal theory.
The mesons in the atom should not have mass, otherwise the inertial motion of the meson mass will break up the atomic structure and cause the collapse of the physics building.
It is the existence of Yukawa coupling that allows this situation of mesons to be explained:
When a meson is inside an atom, it will move along the eight-dimensional atomic structure as a point in space, and it can gain mass on its own after being detached.
Think of this.
Zhao Zhongyao also had an idea.
yes.....
The gauge field belongs to the gaugeable field theory.
According to mathematical definition.
As long as a certain concept is a field theory, its Lagrangian is invariant under certain types of group transformations.
So if you combine gauge symmetry and spontaneous breaking...
Then there may be some changes in the longitudinal or transverse degrees of freedom of the gauge field...
Think about it.
Zhao Zhongyao picked up the pen again.
This time, he planned to start from the simplest field to deduce.
This chapter is not over yet, please click on the next page to continue reading! That is...
The electromagnetic field of SU(1).
Same as before.
Zhao Zhongyao first wrote down a Lagrangian, which is the standard first step in almost all particle physics derivation processes:
L=1/2(??)2?m2?2?mλ?3?λ4?4 m24λ.
Next consider a scalar field with two components:
?=[?1/?2].
Ever since,
The Lagrangian becomes L=1/2(??)2 1/2m2?2?λ4(?2)2 - this potential looks the same as the copper hot pot mentioned before.
And because O(2) and U(1) are local isomorphisms, the U(1) symmetry is also a continuous symmetry.
“Then let ?=12(?1 i?2), then ???=12(?12 ?22), and the Lagrangian becomes: (6)L=????? m2????
λ(???)2, it is invariant under U(1) transformation?→eia?, so it has continuous U(1) symmetry..."
"After dividing ? into ?=peiθ through polar coordinates. The Lagrangian is L=(?p)2 p2(?θ)2 m2p2?λp4, and the vacuum expectation is p=ν=m22λ, θ=0.
....do the transformation p→x ν..."
"The Lagrangian becomes L=[(?x)2?2m2x2?4mλ2x3?λx4] m22λ(?θ)2 (x2 m2λx)(?θ)2..."
"The first part is the kinetic energy term, mass term, and self-coupling of x, and the third part is the interaction of the two fields."
"And the second term is just the kinetic energy term of θ and has no mass, so it is a massless boson produced by the spontaneous breaking of U(1) symmetry..."
"Then the next step is to consider a vector boson that has no mass, and its Lagrangian L=?14FμνFμν..."
"Couple it with the scalar field ? above, and replace the ordinary derivative ?μ with the covariant derivative Dμ = ?μ?iqAμ, where Aμ is the gauge potential of the original massless vector boson..."
"And then so and so...and so and so..."
Looking at Zhao Zhongyao writing quickly on the paper, Xu Yun's face looked a little dull.
What a pity.
This time, his idea was just to let Zhao Zhongyao and the others discover Goldstone's theorem...
The result was unexpected.
When Zhao Zhongyao and the others saw that Xu Yun's kick was not strong enough, they grabbed Xu Yun's collar and threw him back, then went up and kicked him harder.
Now the fun will be great...
Even in a sense, this jio is even more outrageous than dark matter.
Mentioned earlier.
In the early days of particle physics there was a model called the Southern Model.
Its proposer was Neon Man Nanbu Yoichiro, who was considered one of the top contenders for the top number one living physicist when he was alive.
Although objectively speaking, he is half a step behind Yang Lao Weinberg and others, but his ability can be seen from this.
Just like the Chinese people have their blessings for Mr. Yang, many Neon people also firmly believe that Yoichiro Nanbu can be ranked number one in the world when he is alive.
Of course.
There are also many people who blame Nannan Yoichiro, and this is the same in every country.
In this period.
The concept of spontaneous symmetry breaking has become popular in the field of superconductivity. Yoichiro Minami was the first to introduce it into particle physics at the end of this year, which led him to discover the phenomenon of spontaneous symmetry breaking in strong interactions - to be precise.
It is a spontaneous breaking of chiral symmetry.
At the same time.
A year later, Geoffrey Goldstone of the United Kingdom studied that the steady-state solutions could be connected by U(1) phase transformation, and proposed the massless Goldstone mode.
Finally, the two were combined to derive the Southern-Goldstone theorem.
The content of the Nambu-Goldstone theorem is very simple, that is, there must be zero-mass Bose particles after the continuous symmetry is spontaneously broken.
This particle is called a Goldstone boson. For example, Yukawa Hideki's pion is a Goldstone boson that corresponds to approximate chiral symmetry breaking.
But there is a very fatal problem with the Southern-Goldstone theorem, that is...
The mass of gauge particles is a property that is not allowed by symmetry.
Because in the spontaneous symmetry breaking Nanbu-Goldstone theorem, the gauge field still exists.
This also means that local gauge symmetries are preserved - different gauges can be connected by a Lie group transformation.
It’s just that the overall gauge symmetry of the Lagrangian is due to the non-zero expectation of the field in vacuum (the second sentence of Zhao Zhongyao’s calculation), and the quantum field theory does not select the linear superposition of degenerate states as the ground state, which leads to the Lagrangian density.
The gauge symmetry is broken after selecting a specific ground state.... That is, the new Laplace density obtained by perturbating around the ground state does not have the overall gauge symmetry.
But due to local gauge symmetry, the gauge field still exists.
Give another example.
Room temperature superconductivity is very popular recently.
It is precisely because of the disruption of U1 caused by Bose condensation in superconductors that the Maxwell equations of photons will change, thus exhibiting the Meissner effect.
Of course.
Although there are problems with the Southern-Goldstone theorem, it is a good introduction for rabbits.
According to Xu Yun's plan.
After understanding the Southern-Goldstone Theorem for a certain period of time...about two years or so, the rabbits will figure out its shortcomings and come into contact with an advanced version of the concept:
Higgs mechanism.
That's right.
Higgs mechanism.
This famous physics framework is optimized from the Southern-Goldstone theorem.
I won’t go into the specific derivation process of the Higgs mechanism. After introducing it, many people will have to think hard to explain its physical meaning directly:
This chapter is not finished yet, please click on the next page to continue reading the exciting content! In the standard model.
Except for the three weakly interacting gauge bosons, and other basic fermions except neutrinos, they are all directly given mass through the Higgs mechanism.
At the same time, if the mass term is written directly for W and Z gauge bosons, it will violate gauge symmetry, so they also need the Higgs mechanism to be established.
If fundamental particles are human beings, then the Higgs mechanism is clothing.
True.
For primitive society, it doesn't matter whether you wear clothes or not, but in modern society... what would it be like if everyone didn't wear clothes?
It's exciting, but social order and normal production and life are definitely out of the question.
The importance of the Higgs mechanism is evident.
It's just that in the original history, the development process of the Higgs mechanism was very complicated, and it can even be said to be a bit stumbling.
At that time, Goldstone's theorem encountered great controversy after it was proposed in 1962, and even received death threats.
Because theoretically, the case of zero-mass particles is different from the case of heavy-mass particles. Zero-mass particles are easy to make, or their existence can be inferred from the lack of energy or momentum.
However, the physics community at that time could not find any examples of zero-mass particles, so this theory was opposed by Walter Gilbert, the later Nobel Prize winner in Chemistry.
Then five years later.
Higgs proposed the Higgs model.
He said that if the theory of local gauge invariance and the concept of spontaneous symmetry breaking are connected in a special way, then gauge bosons will inevitably gain mass.
Another year.
Weinberg and Abdul Salam independently applied the Higgs mechanism to break the electroweak symmetry, and believed that the Higgs mechanism could be incorporated into Glashow's electroweak theory.
However, these epoch-making papers on the spontaneous breaking of gauge symmetry did not initially receive the attention of the academic community.
Because most physicists believe that non-Abelian gauge theory is a dead end and cannot be renormalized.
This situation would not turn around until ten years later, when Gerald T. Hooft (the little old man who appeared at the original dark matter press conference) published two papers:
He proved that the Yang-Mills theory can be renormalized, both for zero-mass gauge bosons and for massed gauge bosons.
Since then, physicists have begun to accept these theories and formally bring them into the mainstream.
So why is it said that T. Hooft indirectly made Weinberg, and Weinberg indirectly made Yang Lao, the reason is here.
As for the particle that can completely prove the Higgs mechanism...that is, the only scalar boson at present, it will not be truly discovered until 2012.
Moreover, the mass of this thing is 125GeV, and the required collision capability is 300GeV or higher. No matter how European you are, you cannot collide it with 80MeV equipment.
Therefore, Xu Yun has always been in a semi-tangled state about the Higgs mechanism. After all, the current history has been a bit full for him...
When he wants to come.
It might be better if the rabbits could think of the Higgs mechanism three or four years or even five or six years later.
After all, at that time, I was not sure whether the neutron bomb could explode Xu Yun, but the atomic bomb and the hydrogen bomb had definitely exploded successfully, so the load on various equipment should be easier.
Although the cost of doing this is probably that this part of the world will lose its international voice and miss out on two or so awards.
But the stratoton model...that is, quarks can give rabbits the right to define at least 44 types of particles, so it is acceptable to give up the Higgs mechanism.
But I didn’t expect that Zhao Zhongyao said he could accept the eggs, I want them all!
It can only be said that the reality is much bolder than Xu Yun imagined...
Just this way.
The rabbits will definitely have to put a lot of effort into the accelerator.
Judging from the current domestic situation, there is a situation that must be optimized by Xu Yun.
And if this move comes out, then this copy itself will really be involved in all aspects and 360 degrees...
At the same time, Xu Yun's heart was complicated.
The capital is thousands of kilometers away.
A green train also set off quietly.
What needs to be mentioned is.
Apart from some cargo, the car only carried...
A passenger.
.........
Note:
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