Chapter 150 Solving the Mystery of the Proton Radius

In the office of Professor Deligne at the Institute for Advanced Study in Princeton, Xu Chuan finished an afternoon of study.

He put down the ballpoint pen in his hand, moved his head, stretched his waist, and his joints suddenly made a crackling sound, attracting the attention of other people in the office.

This scene has been the norm here for nearly a month.

Everyone who came to visit Professor Deligne knew that he had accepted a new student and was currently studying with him.

Some people were very curious about Deligne's new student. Obviously, this old professor stopped teaching students in person a long time ago, so why did he accept another student this year.

Some people who knew the inside story were amazed in their hearts. Obviously, he had already stood at the top of the mathematics world, but he still chose to return to campus to study hard. His perseverance and far-reaching dreams made people look forward to it.

In the office, Xu Chuan did not care about the eyes of others, and sorted out the study books, notebooks and manuscripts on the table.

In the past month, he has gained a lot in mathematics, not only in number theory and differential equations, but also some basic knowledge in 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 "Draft Program" and "Theory of Prototypes".

These works were compiled by the Pope and other mathematicians in the mathematics community.

But unfortunately, because his research was used in military wars, the Pope in his later years almost recalled all the copyrights of his books.

For the mathematics community, the manuscript in Deligne's hands is no different from the manuscript before the Bible was formed. Its value is inestimable, 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 manuscript about functionals. The manuscript paper was not thick, only a dozen pages, but it made him ecstatic.

Nothing is more valuable than this.

It's just a little regrettable that he couldn't read the manuscript immediately. This masterpiece written by Pope Grothendieck himself was in French.

And he didn't learn French and couldn't understand this work.

But it doesn't matter. It's just a language. It's not difficult for him to learn. It will take at most one or two months.

"Teacher, starting tomorrow, I need to take a vacation for a while."

After packing up his things, Xu Chuan walked to the old man in front of the desk with his backpack and asked.

"Of course."

Deligne nodded and agreed to his request directly, without even asking how long the vacation was and what he would use it for.

If it were other students, he might ask how long the vacation was and what it was for.

But if it was the student in front of him, there was no need for this.

Although the student in front of him had only been studying with him for a month, he had already seen the disciple's desire and love for knowledge.

Such a person will not lose his direction and goal even if no one supervises him.

After returning from the tutor's office, Xu Chuan did not go back to the dormitory immediately, but went to the supermarket to buy some food, canned food, instant food, fruit, etc.

He planned to stay at home for the next few days and solve the calculation method of the "proton radius mystery" in one go.

Mathematics is endless, but the work on the mystery of the proton radius has been slowly improved for a month and is now approaching its end.

In order to ensure that there are no problems, Xu Chuan chose to take a full period of time to concentrate on making a demonstration of the previous calculation process and perfecting the final conclusion.

He gave himself a week. A week, plus the previous work, should be enough.

After buying 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 manuscripts related to the "mystery of the proton radius" and started to check them completely from the beginning.

He checked very quickly, and his eyes flowed on the paper once, and he did not check them carefully one by one.

Because these things have long been familiar to him, he can know whether there is any problem with right or wrong after a slight glance.

But occasionally, Xu Chuan would stop his eyes and pick up the pen to calculate on the manuscript paper.

These are some slightly flawed or cumbersome places left over from the 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 calculation.

He would not give up if he could achieve further perfection.

It took several hours for Xu Chuan to sort out the manuscript paper with the calculation method of the "proton radius mystery" from beginning to end, and then he continued to improve it along the nodes.

Although this was time-consuming, it also had its benefits. On the one hand, it could ensure that there were no problems in the previous process, and on the other hand, it allowed his mind to be perfectly adjusted to the calculation method of the "proton radius mystery".

It was like exercise. Before intense exercise, warm-up exercises could effectively improve the body's cell activity.

Time passed little by little. For a whole week, except for occasional outings for meals and purchasing supplies, Xu Chuan never stepped out of this small room of less than 20 square meters.

Using mathematics to analyze the puzzle of the ‘proton radius mystery’ was much more difficult than he had imagined, especially when he was finishing, he encountered a rare atomic elastic scattering interface charge interference problem.

This is a typical physics problem. If you don’t understand particle physics, you can’t start at all.

But fortunately, physics is his profession. In the end, Xu Chuan successfully solved this problem using the Fourier transform of the three-dimensional spatial distribution of proton charge.

It took two or three days longer than expected, and with the help of the previous few months of work, he finally completed the work.

The ballpoint pen in his hand dropped the last dot on the manuscript paper:

[Some new formulas for the properties of electrons and protons and their physical meanings Energy-charge ratio formula: mC/q=1/2εEds∫.=1/24πrεEr/4πrεE]

[.]

[This method is used to calculate the experimental data measured by the spectroscopy experimental method and the scattering experiment of charged particles and protons.]

[The proton body (with a radius of Rp=7) performs a circular motion (i.e., the second-level spin motion) associated with the de Broglie wave at a quarter of the speed of light around a radius of Rp, =0.8414×10-15m±0.0019fm.]

[The second-level spin motion of the proton body forms a proton spin body (with a radius of Rp, =0.8414×10-15m±0.0019fm ), the circumference of one movement is equal to one de Broglie wavelength when the proton moves at a quarter of the speed of light. 】

The ballpoint pen in his hand sketched out the final information on the manuscript paper, and Xu Chuan stared at the manuscript paper on the table with a shining eye.

After four or five years, he finally perfected this method thoroughly, and the physics community also has a new method to calculate the proton diameter, a "pseudo-first-principle calculation formula" based on the first principles and mixed with some experimental data.

As for the pure first-principle precise calculation of the proton radius data, no one in the entire physics community can do it yet.

Xu Chuan has not tried it, and he doesn't want to spend all his time on it. Unless it can make more amazing discoveries in the proton radius, it is not worth it.

At present, most of the physics community's research on Discussions on atomic structure all rely on the much-criticized Bohr model, in which electrons move in circles around the nucleus.

That is, in the common perception, the structure of atoms should be like the solar system, with electrons orbiting the nucleus (the sun) like planets.

But quantum mechanics, as a stepping stone to physics, gives us a more precise and strange description.

"Electrons do not orbit the nucleus!"

From a quantum mechanical point of view, electrons are a kind of wave, and they only have the properties of particles when we do experiments to determine their positions.

When electrons orbit atoms, they exist in the form of a superposition of particle and wave states, and the wave function contains all the probabilities of their positions at the same time.

Measurement will cause the wave function to collapse, thereby obtaining the position of the electron. Do a series of these Such measurements and plotting different positions will produce fuzzy orbital trajectories.

That is, the electron can appear anywhere in the nucleus, even in the middle of the proton.

It sounds incredible, but from the perspective of quantum mechanics, it is indeed possible.

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 fuzzy, just like a cloud containing three drops of water.

Since the boundary of the "cloud" is fuzzy, how can the diameter be determined?

Physicists rely on charge density to do this, similar to the density of water molecules in the cloud. If 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.

The 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 easy to imagine how difficult it is to measure such a boundary.

However, if there is a demand, someone will definitely solve it. The radius of the proton was estimated early in the development of physics through mathematical methods. Then, with the passage of time and the development of various high-precision physical equipment, this number was accurately measured and finally determined to be 0.879± 0.011 fm femtometers (1 femtometer = 10^-15 meters).

Of course, this is just the "average" taken from many different measurements in the world, and sufficient error conditions have been considered.

Before 2010, this number was adopted by CODATA (International Committee for Scientific and Technical Data) and determined as the radius of the proton.

But later, in 2010, the meson spectroscopy method challenged this value.

In an experiment by physicists at the Max Planck Institute for Quantum Optics, they used muon hydrogen, replacing the electron orbiting the nucleus with a meson as the experimental material.

Because it is nearly 200 times heavier than the electron, its orbit is much smaller, so the probability of it being inside the proton is much higher (10 million times).

And because it's much closer to the proton, this makes the measurement technique 10 million times more sensitive.

This team of physicists originally just hoped that the proton radius they measured would be roughly the same as in previous experiments, making the number of 0.8768 femtometers more certain.

At that time, no one thought that there would be any accidents in this experiment. After all, theoretically, there is no difference between electrons and muons 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 Science and Technology Data Committee (CODATA), and the lowest was even as low as an astonishing 0.833 femtometers.

Even if the influence of energy level changes caused by the protons outside the nucleus is removed, and the average number and error are taken, the radius value is 0.84184± 0.00067 fm.

The result of this experiment caught the researchers at the time off guard, after all, the radius of the proton involves the base of the physics building.

After the results were released, more physicists invested

But since then, more spectroscopy experiments have further confirmed the small proton radius.

Experiments in various countries have shown that the radius of the proton should be smaller than before.

What is puzzling is that the proton radius obtained through the scattering experiment has always remained at around 0.8768 femtometers.

That is to say, the two different test methods have a 5% difference, and this 5% difference 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 the ballpoint pen in his hand, went to the bathroom to wash his face, and then threw himself on the bed. After a while, the sound of fine snoring sounded.

In order to perfect the method in his hand, he has not slept for more than 30 hours. The closer he is to the end of the mystery, the more excited he is, which is enough to fight against physical fatigue.

Now that the result is finally obtained, the thin thread hanging in his mind has finally broken.

This sleep, Xu Chuan slept directly from 4 pm to 3 am the next day before waking up.

Getting up, washing, Xu Chuan took a towel and wiped his wet hair while walking to the desk.

The messy manuscripts on the desk record what kind of trial this place has experienced before.

Picking up a piece of manuscript paper from the table, Xu Chuan's eyes fell on the final answer.

According to the results calculated from the current data, a small proton radius will be the answer in the particle physics community.

People have observed through countless experiments that the charge radius of the proton is not as large as imagined.

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 the error comes from, but mathematics will not lie, and the problem does exist.

Thinking of this, Xu Chuan raised a smile at the corner of his mouth.

This answer, if released, will probably cause an uproar in the entire physics community.

After all, nowadays, there are many people who think that the proton charge radius is a large radius, that is, 0.8768 femtometers.