After hearing what Xu Yun said about the merger of two black holes.
Yang Zhenning's answer no longer came from the microphone, and instead there was the sound of rustling pen calculations.
Throw the ball into the black hole, and then the two black holes merge.
The two are similar at the level of [behavior], that is, they are two things that are close to each other and integrated into one, but their importance is completely different.
The former is considered heterosexual and is barely common, while the latter is equivalent to male ketone.
If a small ball is thrown into a black hole and there is an increase in entropy due to the radius, then theoretically the same should be true for the merger of black holes.
That is...
Both the surface area of the black hole and the entropy of the black hole will increase irreversibly as a result.
"...."
This time.
Yang Zhenning's calculation lasted for a full twenty minutes. During this period, because there was no communication in the room, Lu Guangda outside the room couldn't help but open the door and quietly take a look at the situation.
Twenty minutes later.
Opposite the microphone in Xu Yun's hand, a complex sigh quietly sounded:
"Sure enough, in the spin-merging state, the event horizon area of the black hole will increase as the mass increases."
"Xiao Xu, your opinion...is right."
Yang Zhenning's tone was not depressed, but he was extremely emotional.
Although the physics community has not seen the phenomenon of black holes merging with black holes, not even ordinary black holes have been observed.
But anyone with a little brain can imagine that the merger of black holes must not be an instantaneous behavior - this is relative to the observer.
If the two black holes are still at an angle to each other, they will rotate first and then align. This time span may take millions of years or even longer.
So it's like a small ball merging with a black hole.
When two black holes merge, the concept of [radius] must exist.
The radius here is not the radius of classical physics, but a certain thickness-in layman's terms, it is mass.
The above logical progression may seem simple and a bit inexplicable from the perspective of later generations, but again, the perceptions of each era are different.
Just like Aristotle's so-called truth that "the heavier things fall, the faster they fall", it was not refuted by the physics community until the 16th century using large and small ball experiments.
This is true for large and small ball experiments, and the same is true for black holes and balls.
By the way.
Many people have learned in textbooks that Galileo used large and small balls to deny Aristotle at the Leaning Tower of Pisa, but in fact Galileo did not conduct this experiment...
This was actually just a thought experiment by Galileo. Later, Galileo's student Simon conducted an iron ball experiment at the Leaning Tower of Pisa, and it was written into the "Biography of Galileo" by his other student Viviani.
And the results of this double-ball experiment are not ideal in reality. The height of the Leaning Tower of Pisa is 55 meters, and it only takes three seconds for the iron ball to fall to the ground. The difference between the big and small balls is not enough to deny Yaris Dodd - despite Galileo's thought experiment
itself is correct.
His eyes returned to reality.
Of course.
At this time, what Yang Zhenning was feeling was not that he had not thought of such a simple logical principle, but that he was lamenting the results he had come up with:
The event horizon area of a black hole does increase as its mass increases, and it does not decrease reversibly.
And the event horizon area here...can be equated to the black hole entropy.
The equality here is not literal, because as long as the surface area A of the black hole is divided by Planck's constant h squared and then multiplied by a dimensionless number, the entropy of the black hole can be obtained.
Then Yang Zhenning looked at the formula in front of him for a while, and then said to Xu Yun:
"Xiao Xu, according to your idea... I still have two questions I want to confirm."
Xu Yun quickly sat up straight and said:
"You tell me, I will try my best to answer."
Yang Zhenning paused and asked:
"For the first question, although time is limited, I have not done any specific calculations, but based on the mass-energy equivalence theorem..."
"If black holes really have entropy, then there should also be information inside the black hole?—At least limited information?"
Xu Yun nodded and affirmed:
"That's right."
The situation Yang Zhenning mentioned is the Bekenstein limit mentioned earlier, a theory that was proved by one of the few in 2023 together with the black hole area formula.
"..."
Yang Zhenning was not surprised by Xu Yun's affirmative answer. The purpose of raising this question was actually to elicit the last conjecture:
"That is to say...black holes actually follow the second law of thermodynamics?"
Xu Yun took a deep breath, and his chest rose and fell slightly:
"...That's right."
As we all know.
in the original history.
The development of black hole physics is largely related to Wheeler.
As a disciple of Einstein, John Wheeler, like his teacher, also believed that the key to the laws of nature lies in gravity.
However, Wheeler also worked and communicated with Bohr, the master of quantum physics, so he was also a believer in quantum mechanics.
He is a bit similar to a character named Ye Tianshi in ancient times. He had many masters, and eventually he became a big boss by gathering the leaders of all the masters.
In 1967.
Wheeler became very interested in the gravitational collapse objects described by Schwarzschild in 1917: black holes.
Wheeler believed that a black hole is a standard terminal body. No matter what is thrown into the black hole, the disorder of the system will disappear forever, because no object can escape from the black hole.
Many subsequent works have proven that the black hole is indeed a highly ordered ultimate compressor. No matter how chaotic it is, it will be compressed into infinitesimal sizes at the center of the black hole, including... information.
This description is somewhat similar to the atheist's judgment on the concept of "death" - there is no breath of life, and no soul goes to hell and heaven.
But as a student of Wheeler, Bekenstein did not agree with this.
He proposed that perhaps the information did not disappear in the black hole, but was transformed into a part of the black hole.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! However, no one believed in Bekenstein's idea at the time. It was not until Hawking calculated the area law of black holes that it inspired Bekenstein.
So he took advantage of the situation and launched the famous Bekenstein's upper limit, proving that black holes have information and an upper limit of information.
Of course.
At the beginning, Hawking actually did not believe Bekenstein's conclusion. As a staunch supporter of general relativity, Hawking believed that the young man was teasing himself.
At the same time, although Bekenstein had the right idea, his argument was not very accurate and there were many uncertainties in the calculations.
For example, he just said that the entropy of a black hole is proportional to the event horizon area - in physics, direct/inverse ratio is actually an elusive word.
For any proof, physicists require exact proportions.
For example, gravity is inversely proportional to the square of distance, and magnetic field strength is inversely proportional to the cube of distance. So what about black hole entropy?
Whether it is 2 times the area or 1/2 times the area, this number has to be determined.
Just like the extra update in online articles, if the author with fast writing speed has 20,000 words, it will be considered as extra update, and if the author with slow writing speed has 7,000 words, it will be considered as extra update.
But it's very interesting.
Later, Hawking suddenly realized that due to the uncertainty principle of quantum mechanics, black holes really release a little bit of radiation, and it satisfies the formula of black body radiation, that is, Hawking radiation.
in this case.
Hawking instead accepted Bekenstein's upper limit, and relied on his relatively good mathematical skills to help him calculate the thermodynamic relationship of black holes and correct the proportional coefficient to 1/4.
Therefore, this formula is called the Bekenstein-Hawking equation, also known as the famous BK equations.
The time when the BK equations came into being... is fully 14 years later.
So when faced with the results calculated by himself, Yang Zhenning still seemed a little surprised.
"But it's not right..."
I saw Yang Zhenning underlined the [SBH=Akc^3/4?G] formula he calculated, frowned and asked Xu Yun:
"Xiao Xu, apart from mathematics, what is the reason why black holes logically obey the second law of thermodynamics? Doesn't it increase entropy?"
Common sense.
If a black hole has entropy, it should also have a temperature.
If an object has a temperature, it will produce thermal radiation no matter how low the temperature is.
But in this case, there are problems with the theoretical volume of black holes.
More importantly...
It would make supermassive black holes nonexistent.
"Xiao Xu, look."
Yang Zhenning continued to circle the formula a few times and continued his words:
"There is a relationship between particle temperature and particle energy, kT=E=hf, and the minimum frequency f can only be 1 Hz."
"So the minimum temperature can only be T=h/k, and the radiation temperature of the black hole can only be minimum T=h/k."
"That is to say, when h/k=hc/kr, the black hole radius r reaches the maximum value at this time."
"If the black hole radius increases further, it will violate quantum mechanics and the temperature will be less than h/k."
"So according to the black hole entropy theory, the maximum black hole radius can only be the value of c. So what about supermassive black holes? Doesn't it mean that it doesn't exist?"
Although Xu Yun was not around at this time, Yang Zhenning still pretended to be talking face to face.
Do not know why.
Inexplicably, he had a kind of confidence in Xu Yun:
He believed that Xu Yun could understand his thoughts even over the phone.
It was as if...the two of them had communicated face to face at some point.
And just like he said.
According to the radiation formula, there should be a limit to the black hole radius.
The black hole radius is r=2GM/c^2, so it can be calculated that the maximum black hole mass allowed by the black hole entropy can only be M=c^3/2G.
This value is about 10^35 kilograms, which is also the maximum black hole mass allowed by the black hole entropy.
The mass of the sun is about 10^30 kilograms, which is about 10^5...that is, one hundred thousand times the mass of the sun.
But according to Schwarzschild's black hole model, supermassive black holes that are tens of millions or 100 million times heavier than the sun, not to mention 100,000 times, should theoretically exist.
So either there's something wrong with black hole entropy, or...
There are no supermassive black holes.
And it's not over yet.
If there is a problem with the latter, then there must be a problem with the black hole-related theories that support it—at worst, a patch will be needed to correct it or something.
And this kind of correction is bound to change or increase or decrease a certain parameter, so the derivation of the black hole entropy will also cause problems.
In other words.
This is a logical closed loop, somewhat similar to the grandfather paradox in later generations, and belongs to the discussion of who killed whom.
as expected.
Just as Yang Zhenning thought, the person on the other end of the phone, Xu Yun, only thought about it for a short while and then quickly received the answer:
"Mr. Yang, I think... you may have fallen into a misunderstanding."
Yang Zhenning raised his eyebrows and tapped the pen tip on the table several times irregularly:
"What misunderstanding?"
I saw Xu Yun also wrote the exact same formula as Yang Zhenning on the paper, and drew a circle on another parameter:
"The frequency in black hole radiation is not quantum frequency, but... mechanical frequency."
Yang Zhenning's pen tip on the paper suddenly stopped, and his eyes turned back to his derivation process.
Not quantum frequency?
At the same time, Xu Yun on the other side of the phone said:
"Mr. Yang, as you said, the energy in quantum mechanics must be an integer multiple of h. There is no energy quanta of 0.1h, let alone 0.01h energy quanta - the exception is zero-point energy, but we are not doing zero-point energy today.
Discuss.”
"But the black hole radiation spectrum is a continuous spectrum, and the frequencies are not discrete - because black holes and black bodies radiate similarly."
"In addition, this problem can be understood from the formula. The recursion kT=E=hf is actually wrong. The kT=E part refers to the average kinetic energy, and E=hf is a single particle."
This chapter is not over yet, please click on the next page to continue reading! "If you think about it from this perspective, do you think it can be explained?"
Although he was correcting Yang Zhenning's mistakes, Xu Yun did not underestimate the big boss's thoughts at all.
The frequency of black hole radiation is mechanical frequency.
This is an acute problem that has tortured many physicists, and I don’t know how many people have been driven to the point of death by it.
The radiation spectrum of black holes and black bodies is a continuous spectrum, and the frequencies are not discrete, so there is no mechanism that requires the minimum value of ν to be 1.
For example, in the photoelectric effect, electrons can only be emitted one by one, not 1.5 electrons at a time - this is the quantum frequency.
In actual applications, there are many cases where the frequency is less than 1Hz.
For example, the frequency of nanohertz gravitational waves, which is very popular now, is less than 1HZ.
Therefore, even if the blackbody radiation temperature is lower than the lowest energy of a single surface particle, it does not mean that particles cannot be emitted.
As long as the time is extended, there will always be radiation on average. At most, the interval between radiated particles will just become longer.
After all, a black hole is a system with an extreme gravitational field, and it is not the kind of thing that can use one temperature to represent everything.
Give another example.
A simple system with more than two temperatures is LED.
LEDs have different lights, and a color temperature can be calculated according to the blackbody radiation formula.
But which LED surface particles have what temperature when you touch them?
To put it bluntly, the black hole radiation temperature is the color temperature of the black hole's light emission, while the temperature of the average kinetic energy of surface particles is another thing, so the two cannot be regarded as one and then used to establish simultaneous equations.
Although Yang Zhenning's current vision is not as good as Xu Yun's, his ability to understand has not been reduced at all because of his return to China.
Hearing Xu Yun mention this, he suddenly felt as if a window had opened in front of him, so he quickly raised his pen in the face of the sunlight shining into the house:
"...Then add another Boltzmann constant kB balance dimension. Entropy can be defined in traditional thermodynamics as S=∫dQ/T. The upper part is the absorbed heat, and the lower part is the heat source temperature, so the quantity
Tsuna is J/K...."
"If it is a mechanical frequency, then surface gravity must be considered to represent acceleration, and its dimension can be directly considered to be LT? 2."
"In terms of entropy, it can be divided by the square of the Planck length to offset the dimension of the area, and the temperature can be multiplied by one?/c..."
More than three minutes later.
Yang Zhenning picked up the microphone again with some joy:
"Xiao Xu, it's really like this! The two are facing each other!"
"Black holes...actually obey the second law of thermodynamics. They will both increase entropy and evaporate..."
To the end.
Yang Zhenning's tone was filled with endless emotion.
The second law of thermodynamics is an extremely important concept in classical physics.
The proposer of this iron law is Old Tom William Thomson in the 1850 dungeon, and Clausius who appears at the end of the dungeon.
I won’t introduce much about Lao Tang, but Clausius is a very interesting person.
He was the earliest proposer of the concept of entropy. Even at the end of the 19th century, the unit of entropy was "Clausius" with the symbol Cl.
At the same time, this man is also a well-known Mavericks fan in history. The standard handicraft party - the Newton Personal Museum of Cambridge University has more than 30 Mavericks autograph letters that were donated after Clausius' death.
The meaning of the second law of thermodynamics is [Heat cannot automatically transfer from a low-temperature object to a high-temperature object without causing changes in the outside world]
A system starts from state 1 and changes to state 2 through process 1. If there is process 2 that can change state 2 back to state 1 while eliminating the influence of process 1, process 1 is called a reversible process.
All macroscopic processes related to thermal phenomena (phenomena related to the degree of coldness and heat of objects in nature...that is, temperature-related phenomena are called thermal phenomena) are irreversible processes.
Translated into vernacular, this concept means that particles like to spread out.
Even if the total momentum is fixed and the total energy is fixed, the particle still likes to spread out to various possible places.
To put it more simply...it is impossible to create a perpetual motion machine of the second type.
In the later generations of Xu Yun's time travel, there are many expressions of the second law of thermodynamics. In addition to the expressions of Lao Tang and Clausius, they also include Le Chatelier's description, Carla's description, Calas Theodore's description and other similar ones.
Twenty interpretations.
The second law of thermodynamics cannot be proven yet, but it can be verified.
Now that the number of verifications has increased, it has been infinitely close to the [proof] level.
By the way.
Later, Clausius irresponsibly proposed the theory of heat death, which means that when the entropy in the universe reaches its maximum, all other energy in the universe is converted into heat energy, the temperature of all materials reaches thermal equilibrium, and the heat of the universe
lonely.
At that time, there was no energy flow in the universe. In other words, there was no energy that could sustain motion or life.
However, this hypothesis is no longer a mainstream theory. Even in 1872, when all mankind did not know anything about quantum mechanics, Boltzmann used fluctuations to poke the butt of the heat death theory...
.
But although the theory of heat death is somewhat unreliable or arbitrary, the value of heat itself is still very high.
It is a very important part of classical physics. Especially after the concept of information entropy appeared, quantum mechanics was also linked to thermal 2. Although prl has anti-thermal 2 stuff every year, it is finally proved that these
A large part of them are biased toward clickbait.
Some people hate Re Er as much as they hate the theory of relativity, and some people like to take Re Er into philosophical concepts.
And in this current era.
Hot Er is in a very complicated stage, especially after this thing is combined with a black hole.
"Xiao Xu, I won't hide it from you."
I don’t know if he was stimulated by the amount of knowledge today, but Yang Zhenning rarely recalled some things:
This chapter is not finished yet, please click on the next page to continue reading the exciting content! "Back then, when I and I didn't have many conflicts with a certain enemy, I once discussed the relationship between black holes and hot two with him."
"At that time, we agreed that there would be no entropy in black holes. We even discussed whether the universe is a truly isolated system or even a system of its own."
"But now it seems that we are still thinking a little too far."
Xu Yun smiled and did not answer.
Yang Zhenning’s so-called isolated system seems a bit serious, but in fact it refers to a parallel universe or a high-dimensional world.
I didn’t expect that such a Nobel laureate would be so good at a young age.
At least in Xu Yun's personal opinion, there is a high probability that there are aliens in the vast universe, but the theory of high-dimensional civilization is a bit elusive.
Then Yang Zhenning sighed again, not sure whether he was sighing for the years or the knowledge:
"I didn't expect that black holes, which seem to be non-existent, would actually exist."
"If I said this sentence when I was studying, I would be hung up and beaten by the teacher..."
As he was talking, Yang Zhenning suddenly asked with interest:
"Xiao Xu, since black holes have entropy and radiation, do you think some concepts that have been thought to exist actually don't exist?"
"Such as... Singularity?"
Xu Yun was suddenly startled.
Singular point?
The singularity Yang Zhenning mentioned is not something from later generations, but something deduced based on the theory of relativity.
The so-called singularity refers to the point where space-time begins to bend infinitely.
Modern science describes a singularity as infinitely small in volume, infinitely large in curvature, infinitely high in temperature, and infinitely high in density.
According to the derivation of the theory of relativity, there should be a singularity at the center of a black hole.
For example, the black hole at the center of the M87 galaxy, which is 5,500 light years away from us, is the first black hole to be photographed in the history of human science. The singularity of this thing is that 6.5 billion solar masses are condensed into a space smaller than an atom.
, its theoretical value is:
0.0000000000000000000000000000000000000000014M.
This is not the largest black hole. There is also a supermassive black hole in the Milky Way.
Again.
Later generations would refer to it as "astronomical numbers" when discussing how much money a sum of money weighs or how heavy an ear is. The reason is that for any concept related to celestial bodies, the numbers will be so large or small that they subvert your understanding.
As for the singularity not existing...
Xu Yun thought for a while and gave an answer that surprised Yang Zhenning:
"If the singularity does not exist, then quantum mechanics and general relativity should have been unified by then, and mankind should have entered a new stage of development by then."
“Quantum Mechanics and Extensive Phase Unification?”
be honest.
Compared with other content today, Xu Yun's answer is not that shocking.
but.....
Yang Zhenning felt a very special... optimism from Xu Yun's words.
That's right.
optimism.
Yang Zhenning has also discussed with many people in the past the issue of the non-existence of black hole singularities. After all, strictly speaking, this concept is actually the result of the failure of physics.
Therefore, among those people Yang Zhenning came into contact with, most people’s answers were...
If singularities did not exist, then physics would not exist.
Xu Yun's answer is the only one Yang Zhenning has heard that is optimistic...or has confidence in physics.
Think of this.
Another thought emerged uncontrollably in Yang Zhenning's mind:
Xu Yun.....
Where did this person come from?
at such a young age,
Such a wealth of knowledge,
The organization has given him such high trust and even authority...
To know.
This kind of talent is not something that can be cultivated secretly.
There may be some possibility of secret cultivation in professions such as soldiers and doctors, but theorists...
Without sufficient knowledge supply, how could the rabbits cultivate such a character?
It can't be that it was pulled out of the crematorium, right?
However, Yang Zhenning also knew very well that even if he asked this question at this time, he would probably not get an answer from Xu Yun.
Of course.
At this time, Xu Yun was unaware of Yang Zhenning's many psychological activities. At this time, he also had a thought floating in his mind:
After all this, Hawking's job will probably be taken away by him...
.........
Note:
After I was discharged from the hospital, I found that my voice was a little drifting...
