1900: A physics genius wandering around Europe

Chapter 549: Fermi-Dirac Statistics! The Sixth State of Matter! The Academic World is Shocked Again! This is the Best Era!

University of Göttingen, Germany.

Hunt noticed that something was wrong with Fermi recently.

He frowned all day long, as if he was thinking about something.

Recently, a young and beautiful girl came to the Physics Department, and everyone was like a hungry wolf seeing a sheep.

But Fermi remained unmoved and showed no interest.

That day, while eating, Hunt asked with a smile:

"Fermi, don't you like Mayer?"

Mayer is the girl who recently joined Born's research team.

She is not yet a PhD student, but is participating in research as an undergraduate student.

In real history, Mayer proposed a mathematical model that could explain why a certain number of nucleons can make the nucleus stable.

For this, she won the 1963 Nobel Prize in Physics.

It can be said that Maye is a true female academic master.

In this day and age, such women are truly rare treasures.

Those men who have been single for a long time have been drooling over her.

Fermi took a sip of his soup and then said something irrelevant:

"Brother Hong, let me ask you a question."

"Since photons with integer spin do not conform to Maxwell-Boltzmann statistics."

"What about electrons with half-integer spin? What about them?"

Hong Te was stunned after hearing this.

Got it!
Fermi didn't hear a word of what was said about Meyer.

The other person only thinks about physics, not women.

Seeing this, Hong Te stopped laughing.

Through Fermiti's questions, he realized that the other party was studying the latest Bose-Bruce statistics recently.

Quantum statistics is a very popular topic in theoretical physics recently.

It breaks the framework and conclusions of classical statistical mechanics and is a statistical law unique to quantum mechanics.

Hunt thought carefully for a while and said:

"Because photons do not conform to the Pauli exclusion principle, their statistical laws are significantly different from traditional Maxwell-Boltzmann statistics."

"But electrons are real particles. Even though they have wave properties, from a particle perspective, it's no problem to treat them as small balls."

“At present, Maxwell-Boltzmann statistics are applied very well and there are no major problems.”

"Perhaps particles with half-integer spin do not have their own special statistical laws?"

Hunt felt that there was nothing wrong with his logic.

Although the application scope of Maxwell and Boltzmann statistics is atoms and molecules.

However, there is no essential difference between electrons, atoms and molecules; they are all microscopic particles, just different in size.

Electrons and photons are fundamentally different.

Electrons conform to the Pauli exclusion principle, and they cannot be infinitely superimposed at the same position like photons.

Therefore, Hund felt that the statistical laws of electrons should be the same as those of atoms and molecules, and both should conform to the Maxwell-Boltzmann distribution.

This is also the reason why few people studied half-integer spin particles after Bose's theory came out.

Everyone assumes that this type of particle will not behave much differently from atoms and molecules.

The research is of little significance.

But Fermi didn't think so.

"According to the uncertainty principle, the position and momentum of an electron are constantly changing."

“It can’t be reduced to a small ball model like in thermodynamics.”

"So when counting the behavior of a large number of electrons, one should take into account the uncertainty."

Wow!
Hong Te was shocked when he heard this!
He suddenly felt that what Fermi said made sense.

The particle system described by Maxwell-Boltzmann statistics is based on atoms as a template.

For atoms, the uncertainty effect is extremely weak.

Therefore, the McArthur-Boehm statistics can be described approximately.

Atoms do not have the concept of spin, but electrons and protons do have spin.

This is the significant difference between them.

Fermi obviously wanted to make more precise statistics, and extend it to all microscopic particles with half-integer spin.

Hundt said excitedly:
"Femi, I think your idea is great."

"Perhaps you can also propose a new statistical law like Bose did!"

"Unfortunately, I am an experimentalist, and I am not good at this kind of purely theoretical subject."

"The mathematics involved is terrifying to think about."

After hearing this, Fermi smiled slightly.

"Don't worry, Brother Hong."

"I can handle it on my own."

"Besides, Professor Born is here."

Over the next ten days, Fermi was filled with inspiration and immersed in research.

"When observing from a macroscopic perspective, the energy of a system is constant, but when observing from a microscopic perspective, the system may have many different distribution states."

"For example, if there are three electrons in region A and 3 electrons in region B, or if there are five electrons in region A and eight electrons in region B, the macroscopic state of the system they form may be the same."

“But the microscopic distribution of each system is different.”

"Then, the total number of states of the system is based on the uncertainty principle and statistical principles of electrons, combined with parameters such as the electron's charge and mass."

"The calculation can be obtained as"

"Among these different microscopic distribution states, there are always some states that have a particularly high probability of appearing."

"Among them, the distribution with the highest probability of appearing is."

hiss!
Fermi was astounded by the mathematics involved.

It’s too complicated!

"Would that really be right?"

After completing the theoretical derivation, Fermi couldn't wait to find Born to seek advice.

"Professor, please comment on my paper."

When Born saw Fermi, his heart was moved.

The other party was a young man whom he was very optimistic about.

He is one of the few geniuses in the Department of Physics at the University of Göttingen who specializes in theoretical physics.

Born had high hopes for Fermi.

So he took the paper and read it carefully.

The more he looked, the more solemn his expression became.

Half an hour later, Born was shocked.

He was even more excited than when he saw the quantum tunneling effect before.

Because Fermi's achievement was a purely theoretical breakthrough!

The level of quality is naturally higher!
Although Born's research tended to be experimental, he always aligned himself with Professor Bruce in his heart.

Because only theoretical physics can guide the direction of physics!

I have only heard of theory being ahead of experiments by dozens or hundreds of years, but I have never heard of experiments being ahead of theory for too many years.

He stood up excitedly and said:
"Fermi, your paper is absolutely a major achievement."

“You incorporate the uncertainty principle into quantum statistics.”

“This is where the Bose-Bruce statistic falls short.”

"Moreover, I just found through calculation that if you introduce some approximate conditions, your statistics will degenerate into McBo statistics!"

Wow!
Fermi was shocked after hearing this!

It turns out that the famous McBo statistics is just an approximation of a statistical method that he discovered?

This is amazing!
At this moment, Fermi suddenly thought:
"Then for particles with half-integer spin, can we also use McArthur-Bo statistics to analyze them in approximate cases?"

Born said:

"Probably!"

"Let's do the math together."
-
At the same time, inside the Quantum Research Institute.

After reading Bose's paper, Dirac suddenly had an idea. His doctoral research topic was to use statistical mechanics to study white dwarfs.

A white dwarf can be simply viewed as an electron system.

At that time, he had noticed that the traditional McArthur-Boehm statistics could not well explain the statistics of electrons inside white dwarfs.

To this end, he tried to introduce the theory of quantum mechanics into it.

But probability waves and the uncertainty principle had not yet appeared at that time.

Therefore, Dirac's theory is incomplete.

He did not establish a completely new statistical law that applied to electrons rather than atoms.

And now, Bose's paper gave him inspiration.

"Since photons have their own statistical laws, it stands to reason that electrons should also have them."

"And this law applies to all particles with half-integer spin."

Dirac became interested and decided to try to solve this problem.

Just three days later, he derived a completely new statistical law.

"I see."

“The uncertainty principle is needed here.”

Dirac finally understood what the remaining problems of his doctoral thesis were.

After writing it, he took the paper to see Professor Bruce.

After arriving at the office, Dirac said without further ado:

"Professor Bruce, please take a look at this paper of mine."

"It's about the statistics of particles with half-integer spin."

Li Qiwei took the paper, read it for five minutes, then smiled and said:

“Very good results!”

“Dirac, you can publish now.”

There was no emotion on Li Qiwei's face, not a bit of excitement.

For Dirac, this achievement was mediocre and not worth mentioning.

Dirac himself showed no expression.

He just felt that he had done something unremarkable.

Moreover, he had no doubts about Professor Bruce's calm reaction.

"There's nothing to be surprised about with this little thing."

He simply said "OK" and walked out of the office.

Soon, other people in the lab knew about the paper.

Everyone was shocked.

"Wow!"

"Dr. Dirac, you are so strong!"

"You've also discovered a completely new statistical law!"

Dirac was calm.

"Nothing, just a little work, not worth mentioning."

Everyone envied and admired him.

After spending some time together, everyone has become familiar with the character of this extraordinary genius.

If the other person says it's nothing, then it really means it, and don't be falsely modest or pretentious.

For others, discovering this statistical law is enough to take them to the level of physicists.

But for Dirac, his goal was never the sky.

But it is Professor Bruce who is taller than the sky!

An old man in the laboratory sighed.

I remember when Pauli and Heisenberg were around, when they made a major discovery, they would want to shout it out so that everyone in London could hear it.

Look at Dr. Dirac, he is so calm and composed.

However, soon, a dramatic scene appeared.

Not long after Dirac submitted his paper.

1924 6 Month 2 Day.

Fermi's paper is published.

In his paper, he even proposed a new condensed state directly imitating the Bose-Bruce condensation, that is, a form of matter composed entirely of half-integer spin particles.

This is also the sixth state of matter!
At the same time, Fermi also proved that for these two particles with different spin conditions, the McArthur-Bo statistics are an approximation of their respective statistics.

As soon as the paper came out, it caused a sensation in the physics community!

"My God!"

“I didn’t expect that electrons also have special statistical laws.”

“And this is another paper that was born out of the uncertainty principle.”

However, only three days passed.

Dirac's paper was published shortly afterwards.

When the paper came out, everyone was shocked again!

"what?"

"Isn't this a remake of Davidson and Thomson Jr?"

"They discovered the same thing independently."

"It's just that one is an experimental result and the other is a theoretical result."

For a time, this story became a legend in the physics community.

In real history, Fermi and Dirac independently published papers on this statistical law.

But Dirac directly said that this work was done by Fermi, and he himself called it "Fermi statistics."

This is the low-key Dirac, who is unwilling to argue with anyone.

However, later generations still took his contribution into consideration and changed the name to "Fermi-Dirac statistics".

At this point, the two major statistical laws in quantum mechanics officially came into being.

They are an essential part of quantum mechanics.

For convenience, physicists call particles with integer spin "bosons" and particles with half-integer spin "fermions".

In this way, various particles are essentially divided according to their different spins.

This also laid a solid foundation for the birth of particle physics in the future.

Soon, many new results emerged based on the two major statistical laws.

Based on the principles of Fermi-Dirac statistics, Fowler explained a problem that has long plagued the physics community: field-induced electron emission.

Next, Sommerfeld applied the Fermi-Dirac statistical principle to the study of metal electrons.

Suddenly, everyone discovered an interesting phenomenon.

Many of the geniuses who made it onto the leaderboard in the Second Physics Olympiad have now made their mark in the physics community, and are even leading the way.

Dirac, Pauli, Heisenberg, Fermi, Uhlenbeck, Goudsmit
These young people in their twenties are still apprentices in any field.

However, in the most intelligent field of physics, they created the great brilliance of quantum mechanics.

Their thoughts are not constrained by classical physics, and they are able to run wild and thrive in modern physics.

These bizarre theories or concepts are difficult to accept for ordinary scholars, especially the older generation of physicists.

However, for these new generation of geniuses, the magic of quantum mechanics makes them extremely obsessed.

For young people interested in physics, now is undoubtedly the best time.

Even in future Physics Olympiads, it is unlikely that such a large number of geniuses will appear again.

All the essence of human wisdom seems to be concentrated together and bursting out.

Quantum mechanics is becoming more and more perfect.

Although it still has several key issues that have not been resolved.

But quantum mechanics has penetrated into every aspect of physics.

In modern physics, its areas of application and scope far exceed the theory of relativity.

With the efforts of so many geniuses, everyone believes that the future of quantum mechanics is destined to be bright.

A big shot suddenly had an inspiration and felt his heart beating fast.

"This year may be the most extraordinary year in the history of physics."

The quantum frenzy is surging!
(End of this chapter)