In Professor Deligne's office at the Institute for Advanced Study in Princeton, Xu Chuan finished his afternoon study.
He put down the ballpoint pen in his hand, moved his head, and stretched. The joints all over his body suddenly made a crackling sound, attracting the attention of other people in the office.
This scene has been the norm here for the past month.
Everyone who comes to visit Professor Deligne knows that he has accepted a new student and is currently studying with him.
Some people are very curious about the new student Deligne has accepted. It is clear that the old professor stopped teaching students in person a long time ago, so why did he accept another student this year?
Some people who know the inside story are amazed in their hearts. Even though they are already at the top of the mathematics world, they still choose to return to school and study hard. Their perseverance and lofty dreams make people look forward to it.
...
In the office, Xu Chuan did not pay attention to other people's eyes and sorted out the study books, notebooks and manuscript papers on the table.
Over the past month, he has gained a lot in mathematics, not only knowledge of number theory and differential equations, but also some basic knowledge of algebra and geometry.
Not only that, he also saw some of Pope Grothendieck's "posthumous manuscripts" from Deligne, some of which were written in French, including the "Draft Program", "General Theory" and other things.
These writings were compiled by Pope in the mathematical community together with other mathematicians.
Unfortunately, because his research was used in military wars, the pope in his later years almost recalled all copyrights to his books.
For the mathematical community, the manuscript in Deligne's hands is no different than the original manuscript before the Bible was formed. It is of immeasurable value, not only for collection value, but also for endless academic value.
Xu Chuan got a manuscript from Deligne, which was given to him by Deligne. It was a related functional manuscript. The paper was not thick, with only a dozen pages, but he was ecstatic.
There is nothing more valuable than this.
It was just a little regretful that he could not read the original manuscript immediately. This masterpiece was written by Pope Grothendieck himself and was written in French.
However, he had not studied French and could not understand this work.
But it doesn't matter. It's just a language. It's not difficult for him to learn. It only takes a month or two at most.
........
"Tutor, starting tomorrow, I need to take some time off."
After packing his things, Xu Chuan walked to the old man at the desk with his backpack on his back and asked.
"sure."
Deligne nodded and directly agreed to his request, without even asking how long the leave would be and what the leave would be used for.
If it is another student, he may also ask how long the vacation time the other student needs and what he will use it for.
But if it were the student in front of me, there would be no need at all.
Although the student in front of him has only started studying with him for a month, he has already seen this disciple's desire and love for knowledge.
Such people, even if there is no one to supervise them, will not lose their direction and goals.
.......
After returning from his tutor's office, Xu Chuan did not go back to the dormitory immediately. Instead, he went to the supermarket to buy some food, canned food, instant food, fruit...etc.
He planned to solve the calculation method of the 'proton radius mystery' in one go without going out in the next few days.
There is no end to learning mathematics, but the work on the mystery of the proton radius has been slowly improved for a month and is now almost complete.
In order to ensure that there were no problems, Xu Chuan chose to take a complete period of time to focus on making a demonstration of the previous calculation process and perfecting the final conclusion.
The time he gave himself was one week. One week, plus the previous work, should be enough.
After purchasing food and daily necessities in advance, Xu Chuan locked himself in a small dormitory of less than 20 square meters.
.......
In front of the heavy wooden table, Xu Chuan took out all the manuscript papers related to the 'Mystery of Proton Radius' and conducted a complete inspection from scratch.
He checked very quickly, just running his eyes over the paper once, without going through detailed calculations one by one.
Because these things have long been familiar to him, he can tell whether there is a problem with right or wrong at a glance.
But occasionally, Xu Chuan would stop and pick up his pen and calculate on the manuscript paper.
These are some minor flaws, or cumbersome aspects, left over from past calculations. Now, he has a more streamlined method to replace them, which does not affect the final answer, but can optimize the process and reduce the amount of calculations.
If he can further strive for excellence, he will naturally not give up.
After spending several hours, Xu Chuan combed through the manuscript paper in his hand that recorded the calculation method of the 'Proton Radius Mystery' from beginning to end, and then continued to improve it along the nodes.
Although this is time-consuming, it also has advantages. On the one hand, it can ensure that there are no problems with the previous process. On the other hand, it allows his thoughts to be perfectly adjusted to the calculation method of the 'Proton Radius Mystery'.
This is just like exercise. Before strenuous exercise, warm-up exercises can effectively increase the body's cell activity.
........
Time passed like this little by little. For a whole week, except for occasionally going out to eat and purchase supplies, Xu Chuan never stepped out of this small room of less than 20 square meters.
Using mathematics to analyze the "proton radius mystery" was much more difficult than he imagined. Especially at the end, he also encountered a rare atomic elastic scattering interface charge interference problem.
This is a typical physics problem. If you don't understand particle physics, you won't be able to start.
But fortunately, physics is his specialty. In the end, Xu Chuan successfully solved this problem by using the Fourier transform of the three-dimensional spatial distribution of proton charges.
This chapter is not over yet, please click on the next page to continue reading! It took two or three days longer than expected, and supplemented by the work of the previous few months, he finally completed the work.
The ballpoint pen in my hand dropped the last point on the manuscript paper:
[Some new formulas for the properties of electrons and protons and their physical meaning energy-to-charge ratio formula: mc2/q=??1/2ee2ds∫...=1/24πr2ee2r/4πr2ee....]
【......】
[This method is used to calculate experimental data measured by spectroscopy experiments and scattering experiments of charged particles and protons...]
[The proton body (radius rp=7.65x10-19m) performs a circular motion associated with de Broglie waves (i.e., the second level of spontaneous motion) around the radius rp,=0.8414x10-15m±0.0019fm at a quarter of the speed of light.
rotational motion).】
[The second-level spin motion of the proton body forms a proton spin body (radius is rp, =0.8414x10-15m±0.0019fm). The circumference of one cycle of its motion is equal to one de when the proton body moves at a quarter of the speed of light.
Broglie wavelength.】
The ballpoint pen in his hand sketched out the final message on the manuscript paper. Xu Chuan stared at the manuscript paper on the table with shining eyes.
After four or five days, he finally perfected this method. The physics community also had a new method for calculating the diameter of protons, a method based on first principles and mixed with some experimental data.
'False first calculation formula'.
As for the accurate calculation of proton radius data purely from first principles, no one in the entire physics community can do it yet.
Xu Chuan has not tried it, and he does not want to spend all his time on it. Unless he can make more amazing discoveries about the proton radius, it is not worth it.
Currently, most discussions about atomic structure in physics rely on the much-maligned Bohr model, in which electrons move in circles around the nucleus.
That is, in ordinary people's perception, the structure of atoms should be like the solar system, with planets rotating around the sun (nucleus) like electrons.
But as a stepping stone to physics, quantum mechanics gives us a more precise and stranger description.
"Electrons do not orbit the nucleus!"
From a quantum mechanical perspective, electrons are a kind of wave, and it is only when we do experiments to determine their position that they have the properties of particles.
When electrons orbit atoms, they exist as a superposition of particle and wave states, and the wave function simultaneously contains all probabilities of their positions.
The measurement collapses the wave function, giving the electron's position. Making a series of these measurements and plotting the different positions will produce the orbital trajectory of the model lake.
And this strangeness of quantum physics also extends to protons.
The proton is composed of three charged quarks, which are bound together by the strong nuclear force. But its boundaries are model lakes, just like a cloud containing three drops of water.
Since the boundary of the 'cloud' is modeled after the lake, how to determine the diameter?
Physicists do this by relying on charge density, similar to the density of water molecules in clouds. Once the density of water molecules is determined to be above a boundary value, the diameter of the cloud can be accurately determined.
The same is true for protons.
A proton is not a ball and does not have an absolutely precise radius. Its radius is the distance from the boundary to the core where the charge density it carries drops below a certain energy threshold.
It is conceivable that it is difficult to measure such a boundary.
However, if there is a need, someone will definitely solve it. The radius of the proton has been estimated through mathematical methods early in the development of physics. Then as time goes by and the development of various high-precision physical equipment, this number has been accurately
It was measured and finally determined to be 0.879± 0.011 fm femtometer (1 femtometer = 10^-15 meters).
Of course, this is just an "average" taken from many different measurements around the world, and sufficient error conditions have been taken into account.
Before 2010, this number was adopted by codata (International Committee on Scientific and Technical Data) and determined as the radius of the proton.
But later, in 2010, meson spectroscopy measurements challenged this value.
In an experiment by physicists at the Max Planck Institute for Quantum Optics, they used meson hydrogen, replacing the electrons orbiting the nucleus with a meson as the experimental material.
Since it is nearly 200 times heavier than an electron, its orbit is much smaller, so the probability of it being inside a proton is much higher (10 million times).
And because it is closer to the protons, this makes this measurement technique ten million times more sensitive.
This team of physicists originally hoped that the proton radius they measured would be roughly the same as in previous experiments, making the number 0.8768 femtometers more certain.
At that time, no one would have thought that there would be any surprises in this experiment. After all, theoretically, there is no other difference between electrons and mesons except mass and lifespan.
However, if there is no accident, there will definitely be an accident.
In this experiment, the proton radius they measured was significantly lower than the value given by the International Committee on Scientific and Technological Data (codata), and the lowest was even as low as an astonishing 0.833 femtometers.
Even if the influence of energy level changes caused by electrons and protons outside the nucleus is removed, and the average number and error are taken, the radius value is still 0.± 0.00067 fm.
This experimental result caught the researchers at the time a little off guard. After all, the radius of the proton involved the base of the physics building.
After the results were released, more physicists pitched in
But since then, more spectroscopic experiments have further confirmed the small proton radius.
Experiments from various countries have shown that the radius of the proton should be smaller than before.
This chapter is not over yet, please click on the next page to continue reading! What is puzzling is that the proton radius obtained through scattering experiments always stays at around 0.8768 femtometers.
In other words, two different testing methods produced a 5% gap. This 5% gap is called the 'proton radius mystery'.
As of today, this mystery has finally been solved.
Of course, the premise is that Xu Chuan's calculation method is correct.
........
In front of the desk, Xu Chuan threw away the ballpoint pen in his hand, went to the bathroom, washed his face, and then threw himself on the bed. After a while, soft snoring sounded.
Both Android and Apple are available.]
In order to perfect the method in his hand, he had not slept much for more than thirty hours. The closer he got to the end of the mystery, the more excited he became, which was enough to resist physical fatigue.
Now that the result has finally been achieved, the thread hanging in my mind has finally been broken.
During this sleep, Xu Chuan slept from 4pm to 3am the next morning.
After getting up and washing up, Xu Chuan took a towel and wiped his wet hair while walking towards his desk.
The messy manuscript papers on the desk record what kind of trial this place has gone through before.
Picking up a piece of manuscript paper from the table, Xu Chuan's eyes fell on the final answer.
Judging from the results calculated based on current data, a small proton radius will be the answer to the particle physics community.
People have observed through numerous experiments that the charge radius of the proton is not as large as imagined.
And this also means that before 2010, the data observed by the entire physics community were wrong.
In other words, there was a huge error in their experimental process, which led to this result.
At present, he still doesn't know where this error comes from, but mathematics does not lie, and the problem does exist.
Thinking of this, Xu Chuan's lips raised a smile.
If this answer is released, I am afraid it will cause an uproar in the entire physics world.
After all, nowadays, many people think that the proton charge radius is a large radius, which is the number 0.8768 femtometers.
