Chapter 286 A challenge to the stars! (Part 2)
"I don't create miracles, because I am a miracle."
Hear what Gauss said.
Xu Yun was stunned subconsciously.
According to his original judgment.
Gauss may incite his own emotions by saying something more inspiring like he did when he talked to Tian Hao before - that is, I don't believe in fate.
When the time comes, maybe my head will get hot and I will impulsively make some promises.
But I didn’t expect
Gauss actually said such a domineering statement?
But at the same time, Xu Yun also discovered.
There seems to be nothing wrong with what Gauss said?
You must know that in later generations, there were no less than a hundred theorems starting with the name Gauss - although many of them were actually given as 'Gauss XX Theorem' in memory of Gauss, there were still quite a few that were summarized by Gauss himself. of.
When he was studying, he was despised by a nobleman, so he took up the subject of modern mathematics and suppressed classical mathematics for a long time.
It can be seen on the mathematical genealogy website MathematicsGenealogyProject.
Gauss currently has 96,947 apprentices and descendants. A Chinese actress with the same name as him expressed great pressure.
There is a joke in the mathematics community that "Riemann was the pseudonym used by Gauss when he published unsatisfactory results."
Although this sentence is a pure joke, it is enough to show the horror of Gauss's research results.
At the same time.
What is even more amazing about Gauss is not his achievements during his lifetime, but the manuscripts he left behind after his death.
The most prolific mathematician in history should be Euler, but the one with the highest quality manuscripts is undoubtedly Gauss - Paul Erdos is a modern figure and will not be discussed.
Gauss died in 1855, but even in 2022, the mathematical community is still studying Gauss's manuscript.
For example, the work of Manuel Bhargava, who won the Fields Medal in 2014, was inspired by reading the chapters related to quadratic forms in Gauss's "Arithmetic Explorations".
This matter was published by Manuel Bhargava in the top journal Annals of Mathematics, doi.org/10.4007/annals.2015.181.2.4.
So for Gaussian.
He is indeed qualified to say "I am a miracle".
Even if he hadn't been a believer, maybe the word "miracle" would have been replaced by the God of Mathematics.
Don't know why.
Xu Yun inexplicably thought of Lao Su again.
They are both at the end of their lives, and they are both obsessed with the stars, but the personalities of Lao Su and Gauss are completely opposite.
Of course there are cognitive barriers caused by different times, but perhaps more of it is the personality differences caused by Eastern and Western cultures.
The East pays attention to elegance and restraint, while the West is relatively more wanton and public.
Xu Yun couldn't say which character was better and which was worse, but he had to admit one thing - he was a little moved by Gauss.
The history of mankind is a history of challenges as well as a history of development from scratch, and China is a leader in this regard.
True.
What cannot be discovered in 2022 will indeed be difficult for 1850.
But this statement is not absolute.
It does not mean that something that cannot be discovered in 2022 will definitely not be discovered in 1850 - there is actually no necessary connection between the two.
Just like something mentioned before.
If the optical path principle of some telescopes is changed.
Then the telescope in 1800 was enough to see stars 180 AU away and below +12.6 visual magnitude.
The perihelion of the possible ninth planet estimated by later generations is about 25-30 billion kilometers, which is theoretically in line with the limit observation distance of astronomical telescopes.
In addition, there are Gauss, Riemann, and Wheat at this time
Maybe
Can you really give it a try?
Thinking about it.
Xu Yun's mood also became slightly agitated.
Looking at all the copies in the past, he has led more than one operation that spanned the ages.
For example, the dispersion phenomenon in the Mavericks copy, infinitesimal series, the development of ketchup, etc.
For example, electrolysis, mercury telescopes and even airplanes in Lao Su's copy.
Another example is the photoelectric effect in today's wheat replicas and the observation of Pluto.
But let's be honest.
Although all the above operations have different levels of difficulty, no matter which one they are, Xu Yun actually understands them all.
That is to say, he knows in his heart that he will definitely succeed - no matter how bad things happen, there is a remedy.
This is not because he can strategize, but because later generations have various models for him to choose from.
But this time.
Later generations did not have any data for him to learn from, so it was a completely uncertain attempt.
But that’s what makes it more interesting, isn’t it?
Think of this.
A trace of determination flashed in Xu Yun's eyes.
He took a deep breath, raised his head and looked at Gauss, and said:
"Professor Gauss, to tell you the truth, the ancestors of Fat Fish did leave some useful things in the field of astronomical observation"
Swish——
The words just fell.
Gauss then came to Xu Yun in a flash. He didn't look like he was about to die before. He stared at him with bright eyes and asked:
"Classmate Luo Feng, are you serious? Did Mr. Fat Fish really leave something behind?"
"."
Xu Yun twitched the corner of his mouth and nodded dryly:
"Of course it's true."
Gauss quickly asked:
"What's there?"
Xu Yun thought for a moment, turned around, pointed at the external 'Tatara' telescope and said:
"The first is the optimization of astronomical equipment. Ancestor Fat Fish designed a drawing that can make the imaging effect of the astronomical telescope more obvious."
Gauss's expression was slightly startled, and he blurted out:
"Optimization?"
Xu Yun nodded, picked up the pen and Zhidao, and drew a sketch:
"The ancestor of Fat Fish is a scholar of heaven and man. After a long period of experimentation, he discovered a light path combination that can increase the observation effect of the telescope without changing the material and diameter."
"This combination requires a very large primary mirror and spherical mirror, and is equipped with multiple mirror blank units."
“Because it requires digging a lot of holes in the inner core area, Feiyu Xianyu named it the ‘An Le Plan’.”
After hearing this, Gauss took the paper and looked at it carefully.
It turned out not long after I saw it.
A soft cry came from his mouth.
The picture drawn by Xu Yun is somewhat different from the standard reflecting telescope. For example, it adds a flat-field lens and changes the focal plane to a flat surface.
Another example is the addition of many hexagonal lenses inside, which seems to require many reflections to achieve a normal image.
That’s right!
Seeing this, some students must have guessed it.
The design drawings given by Xu Yun are exactly the principle images of the Schmidt telescope.
Among the original 1100 copies, due to the limited production accuracy level in the Northern Song Dynasty, he could only produce older combinations such as the first generation Cassegrain.
But now it is 1850, and the level of science and technology is far from what it was in 1100.
And due to changes in the world line, the level of industrial production is even close to that of 1900.
This way.
Xu Yun directly took out the schematic diagram of the Schmidt telescope.
The Schmidt telescope appeared in 1931 and was invented by the German optician Schmidt.
It has been modified and optimized with part of the light path diagram to achieve strong light power, a large visible range, and good imaging quality.
Many observatories in later generations also used Schmidt telescopes. For example, Mike Brown's team discovered Eris with it.
Although later Schmidt telescopes added active control systems and CDD fine screening modules, in fact these devices are mainly used to screen stars and have no impact on imaging.
all in all.
The Schmidt telescope was the ceiling of reflecting telescopes in the astronomical world before the invention of radio telescopes.
The image points everywhere on the focal surface of the Schmidt telescope spherical mirror are symmetrical, and this happens to be the category of Gaussian curvature of the sphere. From the name of this theorem, it is not difficult to see that its summarizer is the little old man in front of you. .
So after just a quick glance at the schematic diagram, Gauss's eyes lit up:
"Good idea! Although there are certain requirements for the glass negative and the processing of the correction mirror is difficult, the imaging effect is good."
Gauss looked like a later monk reciting sutras, with the index and middle fingers of his left hand constantly touching his thumb.
Soon, he simply mentally calculated the optimal magnification of the video:
1.5-2.5 times that of Tatara!
To know.
Although Tatora is inferior to the Berlin Observatory’s treasure ‘hixiv’ (I don’t know how to translate this thing in Chinese), it can at least be ranked among the top three in Europe!
in this case.
The design drawings that Xu Yun can take out at will are twice as many as those of Tatara.
A word popped up subconsciously in Gauss's mind:
So scary!
Then he looked at Xu Yun and said:
"Classmate Luo Feng, I will try my best to find someone to complete the preparation of the telescope. What about other things?"
"Others"
Xu Yun thought for a while and said:
"The second thing is time."
"Time?"
Xu Yun nodded, looked at the observation records that had been sealed again, and explained:
"Professor Gauss, at this point, the earlier observation records are of little use anymore."
"We need more and clearer images of the starry sky - this must be done with the Schmidt telescope."
"So after the telescope is successfully optimized, we need at least one year of new observation records."
"One year?"
Gauss subconsciously touched his lungs and pressed lightly with his thumb.
Then he hesitated for a moment and asked:
"Classmate Luo Feng, is one year enough?"
Xu Yun nodded and said:
"This involves another arrangement, which I will explain to you later. In short, the more images, the better."
Gauss took a deep look at him, took a deep breath, and said decisively:
"No problem, I will write a joint letter with Faraday to persuade as many observatories in various countries to take observation records."
"The discovery of 'Conan's Star' this time should set off a wave of discussion in the astronomical community. Coupled with the optimization diagram of the Schmidt telescope, it is probably no problem to ask for their help."
"So, student Luo Feng, what about the third point?"
"The third point."
This time.
There was an obvious hesitation on Xu Yun's face, as if he was making some calculations.
A few seconds passed.
He gritted his teeth, picked up the pen and started writing on the paper.
After a few minutes this time, Xu Yun raised his head and handed the calculation paper to Gauss:
"Mr. Gauss, these are some formulas derived by our ancestors after calculating the speed of light. They may be helpful to you."
at the same time.
He sighed slightly in his heart:
Sorry, my dear
Gauss took the piece of paper and glanced at it lightly.
Suddenly his pupils shrank, his face changed drastically, and even the calculation paper was shaking:
"This is this?"
See this situation.
Riemann and Mai on the side couldn't help but look at each other, and saw curiosity in each other's eyes.
To know.
Even when he first saw the schematic diagram of the Schmidt telescope, Gauss was not as out of his mind as he is now.
After a while.
Gauss just slowly raised his head, remained silent for a long time, and sighed:
"I didn't expect it. It turns out that hundreds of years ago, Mr. Fat Fish explained the nature of the abnormal precession angle of Mercury."
"What have we, the mathematicians and physicists of later generations, done?"
Taking advantage of Gauss's absence.
Riemann and Xiaomai gently approached him and looked at the contents on the paper curiously.
I saw several equations and some derivation formulas written on the paper that Xu Yun handed to Gauss:
du/dθ+u=GM/h+(3GM/C)u
△Φ=6πM/L
dx^a/dS=-￡aik（dx^i/dS）(dx^k/dS)
That's right.
Presumably Zhong Zhou, a classmate who is smarter than the classmates who can see the principle of Schmidt telescope, has already figured it out.
The formulas given by Xu Yun are precisely the geodesic equations of the second-order asymptotic solution of the general theory of general relativity, the precession angle equation, and the weak field low-speed approximation.
According to the original historical trajectory.
The second-order asymptotic solution is a perturbation solution that was derived several years after the general theory of relativity was proposed.
Not to mention the precession angle equation and the theoretical geodesic equations of the weak field low-speed approximation, which also involve magnetic-like effects.
Based on emotion and reason.
They are not things that should appear at this time. In fantasy novels, they would be struck by five or ten lightning tribulations from the heavens.
But there is no way.
After all, the scientific community's understanding of planets these days only remains in the category of first-level asymptotic solutions.
Although Gauss, Laplace and others have established perturbation theory, there is still a certain distance from the concept of 'perturbation method'.
And even the first-level asymptotic solution given by the perturbation method is still somewhat inaccurate in planetary problems.
Therefore, Xu Yun had no choice but to take out the second-level asymptotic solution.
Without a second-order asymptotic solution, even Gaussian cannot calculate the orbits of trans-Neptunian objects.
As for the precession angle of Mercury mentioned by Gauss
This is a very famous allusion in astronomy.
It’s called Einstein killed ‘Zhu Rongxing’.
Mentioned earlier.
Before the 20th century, Maverick's classical mechanical system provided a concise and elegant theoretical explanation for the operating laws of the universe.
This theory was once so accurate and reliable that Le Verrier discovered Neptune on the tip of his pen just through rigorous mathematical calculations.
It was a memorable theoretical victory in the history of science. When the Neptune predicted by Le Verrier appeared in the observer's telescope as scheduled, people became more convinced of the Newtonian mechanical system.
But while other planets in the solar system are verifying the correctness of this set of mechanical laws with actual operating data, it is Mercury that poses a small problem to scientists:
The actual change in Mercury's perihelion orbit is 38 arcseconds per century greater than the theoretical value obtained through calculation.
In order to explain the 38 arc-second error in the "perihelion precession of Mercury's orbit", Le Verrier speculated that there is an inner water planet within the orbit of Mercury.
In February 1860, this aquatic planet officially had its own name - "Vulcanus", the god of forging in Roman mythology. The Chinese translation is called Zhu Rongxing.
within the next half century.
Zhu Rongxing has become a key target pursued by many physicists and astronomy enthusiasts.
But no matter how hard astronomers try, they can't find any trace of this planet:
The distance between Mercury and the Earth only fluctuates by one astronomical unit. If such a planet really exists, it should not be difficult to discover it in theory.
And just when the astronomical community found nothing.
The old love appears.
He proposed the theory of relativity and explained that Mercury's precession was caused by the sun's gravitational field being dragged by its own rotation, which dealt a fatal blow to Zhu Rongxing.
Just like many weapons that see blood when unsheathed, the theory of relativity wiped out a planet when it first appeared on the scene.
But on the other hand.
Students who understand the theory of relativity should know this.
In fact, after the theory of relativity was proposed, it itself was not 'equipped' with many parameters.
For example, we only know that the curvature of space-time caused by gravity is related to the speed of light, and we also know that the space-time bay at the event horizon of a black hole is curved to reduce the speed of light to zero.
But the speed of light is not the physical parameter that expresses the curvature of space-time. Who knows how much the space-time is curved?
Therefore, later generations of mathematicians established mathematical topological manifolds, observed and calculated many parameters through, for example, the gravitational lens effect and liquid superfluid helium 3.
Substantial evidence like Lao Ai's "killing" of Zhu Rongxing is actually the verification of light from the later total solar eclipse, rather than mathematical derivation.
The time when Mercury's precession angle was actually summarized using mathematical formulas was in 1968, when Lao Aidu passed away more than a week ago.
So theoretically.
If you are lucky.
Some parameters can be calculated to determine their expressions before the theory of relativity was proposed.
Although this probability is ridiculously small, it is not non-existent.
For example, the Runge-Lenz vector involved in high school physics competitions is one of them.
The solutions it obtains when n=2, 3, and 4 are actually completely consistent with the perturbation method.
So on this piece of paper given to Gauss.
Xu Yun directly summarized the reasons for Mercury's precession angle using mathematical formulas, which can be universally applied to any planet in the system.
Don't ask, asking means that the 'Fat Fish Ancestor' is a scholar of heaven and man, and has gained insight into the nature of the world.
Anyway, you see Lao Ai doesn’t object now, right?
Not to mention that with a living mathematical miracle like Gauss in front of him, Xu Yun's behavior was not too outrageous to be honest - after all, he only gave the formula and did not propose the content of the theory of relativity.
This is equivalent to someone solving the Riemann Hypothesis in 2022. The sensation will definitely be a sensation, but it will not be arrested for slicing and breeding.
Then Gauss collected Xu Yun's piece of paper very preciously, pondered for a moment, and then said to Xu Yun:
"Classmate Luo Feng, with these three things you have provided, maybe we can really gain something."
"Well, I will start preparing for the observation as soon as I get back. One year later, I hope we can replicate the glory of tonight."
Seeing Gauss eager to leave the shed, Xu Yun suddenly stopped him:
"Professor Gauss, please wait."
"?"
Gauss frowned when he saw that, like a scumbag who put on his pants and wanted to leave after a date, and asked impatiently:
"Anything else?"
Xu Yun nodded and said:
"There is indeed one more thing, that is, if we want to be able to observe the unknown planet, we still need a helper."
"Who? Peng Serie? Gloria? Kexi? Or is your surname Xia? Let's talk about Zhang?"
".No, he is one of my seniors and a graduate of Trinity College."
"What's your name?"
"Charles Babbage."(End of Chapter)