1900: A physics genius wandering around Europe

Chapter 533 Probability Wave! The most mysterious concept in quantum mechanics! Finally revealed! Shocking! The audience was shocked!
Under the horrified gazes of the crowd, Li Qiwei remained calm and composed.

From today on, quantum mechanics will truly challenge the limits of human cognition.

If you believe it, then you can understand quantum mechanics.

If you don't believe it, you will never understand quantum mechanics.

Everything starts with the third wave.

After scanning everyone present with sharp eyes, Li Qiwei spoke.

"A month ago, Professor Born published a paper. I wonder if anyone here has read it."

“The title of the paper is ‘Quantum Mechanics of Scattering Processes’.”

“It is based on Heisenberg’s matrix mechanics and studies the discontinuous properties of particles by studying their behavior during scattering.”

“One of the phenomena is very interesting.”

"In his paper, Born recorded the probability of a scattered particle appearing in a certain direction."

"I guess he is imitating the research ideas of matrix mechanics on spectral intensity."

Born's expression changed when he heard this.

This paper was written as a supplement to his research on matrix mechanics.

The paper was not even published in Nature, but in a physics journal in Germany.

He didn't expect that he would be noticed by Professor Bruce.

For a moment, Born was a little flattered.

But he was a little confused.

“Is there anything special about this paper?”

Apart from Born himself, Heisenberg was the only person present who had read the paper.

However, he was also confused and didn't know what Professor Bruce meant.

He glanced at Born, who nodded slightly, then shook his head.

Neither of them understood.

As for the others, none of them had read the paper and shook their heads.

Because obviously, this is a paper related to matrix mechanics.

While wave mechanics is popular, fewer people are definitely paying attention to it.

At this time, Heisenberg said:

“Professor, I’ve read that paper.”

"But how does it relate to the third wave you mentioned?"

Li Qiwei smiled slightly and continued:

"Of course it does."

“Born himself did not realize how shocking his paper contained.”

After that, Li Qiwei opened Born's paper.

"Everyone, please take a look."

"In the scattering experiment, Born simply listed the probabilities of the various directions of the particle as vectors."

“He wanted to study this concept through the matrix.”

"but."

"If I introduce the concept of wave mechanics at this point."

Suddenly, Li Qiwei raised his voice, as if possessed by a familiar shadow.

Everyone immediately felt a terrifying pressure coming from the mysterious oriental teacher.

"Watch out, I'm about to transform!"

"I linked the probability of the direction in which a particle will scatter to the wave function ψ in the wave equation."

"Then we will get this result: the probability of a particle appearing in a certain direction is proportional to the square of the wave function ψ!"

"This means that the electron wave described by the wave function ψ is not a mechanical wave like a water wave."

"ψ describes the probability wave of the electron's distribution in space!"

“So I think Schrödinger’s idea that there were only waves was wrong.”

"Electrons have the dual nature of wave and particle, but the wave nature is not the known mechanical wave or electromagnetic wave."

"It's a completely new wave, the third wave, the [Probability Wave]!"

"The square of the modulus of the wave function |ψ| represents the probability of an electron appearing at a certain position in space at a certain moment!"

"That is: the probability of an electron appearing in various places is like a wave!"

boom!
As soon as the words fell, the whole audience was shocked!
Everyone opened their eyes wide, as if they had seen the most incredible thing in their lives.

“Probability is a wave?”

"Oh my God! How is this possible?"

Born's eyes seemed to be spitting fire.

That is the fire of wisdom!

He didn't expect that his paper would come to such a shocking conclusion.

this is too scary!

De Broglie was shocked!

Professor Bruce has just proved that wave mechanics and matrix mechanics are equivalent.

As a result, Schrödinger's wave theory was abandoned.

Professor Bruce supports the wave-particle duality!
This is the same as de Broglie.

It’s just that the wave in this wave-particle duality is really a bit weird.

De Broglie could not imagine how the probability of an electron appearing in various places could be a wave.

Waves are functions that describe the motion state of matter.

Probability is not motion, so how can it form waves?
Not only de Broglie, but everyone was puzzled.

Suddenly, Planck, Einstein, Bohr and many others looked shocked.

"Probability?"

They thought of something old and relevant.

At the second quantum theory conference, Bohr expounded the core of the old quantum theory: the quantum orbit model.

In Bohr's theory, electrons have the concepts of orbits and transitions.

Electrons can jump from a low energy level to a high energy level, and also from a high energy level to a low energy level.

At that time, someone asked:

"When an electron is jumping, how does it know which energy level it is jumping to?"

"What physical factors determine the transition behavior of electrons?"

Bohr did not answer.

Finally, it was Professor Bruce who came up with an extremely bold idea:

"Electrons jump randomly in a probabilistic way!"

At that time, no one agreed with this view.

Because it's so unbelievable.

How can something as vague as probability be used to describe the precise physical world?
Although there are also probability statistics in thermodynamics.

But that is a macroscopic analysis of the thermal motion of a large number of molecules.

Essentially, the motion state of each molecule is definite.

However, due to the large number, it is impossible to list all of their motion equations, so they are described using probability statistics.

Therefore, the probability in thermodynamics and the probability of electron transition are two completely different concepts.

The former is easy to understand, while the latter subverts people's three views.

Until today, the physics community has not reached a consensus on the probabilistic behavior of electron transitions.

Fortunately, the transition itself does not have much impact on the application of the old quantum theory.

Therefore, everyone tacitly agreed not to discuss the issue, and it remains to this day.

But today, Professor Bruce proposed an even crazier idea: the wave nature of electron waves is actually probability waves.

Probability theory is back!
Shocking!

This has exceeded everyone's imagination.

People had no idea what kind of physical picture that was.

"Probability is probability, how can it be related to waves?"

In the crowd, Schrödinger was completely stunned.

He simply couldn't believe what he was hearing.

"Professor Bruce directly denied the wave theory." "The wave-particle duality is the orthodoxy!"

“And he also proposed the astonishing concept of probability waves.”

"Impossible, absolutely impossible!"

Schrödinger fell into self-confusion.

At this time, Born was extremely puzzled and could not help asking:
"Professor Bruce, I still don't quite understand."

“How can probability be a wave?”

Born was probably the most excited person on the field.

But he is also the calmest.

He is very clear about the papers he published.

It has absolutely nothing to do with probability waves.

It was completely imagined out of thin air by Professor Bruce relying on his terrifying physics intuition.

He was worried that his humble work could not carry such wild and imaginative ideas.

Li Qiwei looked at Born and felt emotional.

In real history, Born is far less famous than Bohr, and even non-professionals have never heard of him.

But for the top physics giants, Born is actually the person who made the greatest contribution to quantum mechanics in the strict sense.

All this is because of the probability wave he proposed!
This theory is really too important.

It can be said that it is the foundation of the entire quantum mechanics.

The core of the Copenhagen interpretation is based on the concept of probability waves.

And now, Li Qiwei was excited.

"In this life, I will bear the responsibilities of all the causes and consequences of quantum mechanics."

He then went on to explain:
"I once mentioned at the Second Quantum Theory Conference that electron transitions are probabilistic behaviors."

"Unfortunately, the academic community has not yet recognized this."

“When I was reading Born’s paper, the idea came back to me.”

"This time, I am confident that I will not be wrong!"

Wow!
Everyone was shocked!

How domineering this is!
"Let me give you a vivid example to illustrate the probability wave."

"Suppose there is an electron here now."

"It's not a real wave propagating through space, like a water wave, as Schrödinger believed."

"The electron itself is still a particle, but it can appear [at the same time] [anywhere] in space." (Remember these two words)

"At this point, someone might ask: So where do the electrons appear at points A and B?"

"The answer is the wave function ψ."

"Based on the wave equation, we can find the wave function ψ of the electron."

"ψ itself does not represent the probability of the electron appearing, it is just a function that describes the electron system."

"|ψ| represents the probability of the electron appearing at point A and point B."

"For example, we calculated that the probability of the electron appearing at point A is 0.9, and the probability of appearing at point B is 0.2."

"Then we can say that the probability of the electron appearing at point A is greater than the probability of appearing at point B."

"What's even more amazing is that the waves formed by this probability distribution can interfere and diffract like real waves."

"So, Schrödinger mistook probability waves for real waves."

“But actually, it’s not.”

"The probability that the electron is at point A is x, the probability that it is at point B is y, and the probability that it is at point C is z"

"The mathematical form of the distribution of these probabilities is the same as the wave function form of mechanical waves and electromagnetic waves."

“Therefore, Schrödinger naturally regarded the probability wave of electrons as a mechanical wave.

"Through this theory, we can explain the question that Bohr just raised."

"In wave mechanics, electron waves permeate the entire atomic space. Schrödinger was right about this."

"Then why do discrete energy levels appear?"

"It's simple, because the energy levels we observe are just the places where the probability of electrons appearing is the highest."

"So, macroscopically, it behaves as if electrons have discrete energy levels."

“But it’s not.”

"The energy level itself does not exist, it is just a region."

"Electrons don't have to stay in a specific orbit. They can appear anywhere in the atom, but the probability of appearing in each place is different."

"Everyone, please take a look."

Li Qiwei drew a picture as he spoke.

"Take the hydrogen atom as an example. The probability of an electron appearing in various places around the nucleus is as follows."

"Each black dot represents [an electron appears here], and the density of the black dots represents the probability of the electron appearing."

"The denser the black dots, the greater the probability that electrons will appear in this area; the sparser the black dots, the smaller the probability that electrons will appear in this area."

"These black spots look like a negatively charged cloud surrounding the nucleus."

"So, I call it [electron cloud]." (This is where the concept of electron cloud comes from)
"Electron clouds replace the concepts of orbitals and energy levels in the old quantum theory."

"Electrons are not like we imagine, in the form of a small ball moving in various orbits."

"Electrons fill the entire electron cloud."

"Wherever the electron cloud covers, there is a probability that the electron will appear, but the probability is different."

"That's my explanation of probability waves."

quiet!
Deathly silence!

The room was so silent that you could hear a pin drop.

Everyone was stunned with shock, as if time had stood still.

Unbelievable!
Unbelievable!

incredible!

Even: It feels like Professor Bruce is talking nonsense!

"Oh, God!"

"Is this possible?"

"This is absolutely impossible!"

"This idea is no longer shocking, it transcends this world and this world!"

"Professor Bruce is horrible!"

"This theory is simply not something that humans can come up with."

Soon, the whole audience was shocked!
A huge exclamation broke out in the room!
The concept of probability waves drove everyone crazy.

In summary, it contains three core ideas:

First, microscopic particles such as electrons have the wave-particle duality, and the wave nature does not refer to real waves, but rather to different probability distributions.

It’s just that the mathematical expression of probability distribution is the same as the wave function in the conventional sense, so it is figuratively named probability wave.

For example, assuming that the wave function of the mechanical wave is in the form of f=x+1, then the probability distribution of the electron's appearance position is also f=x+1.

Second, the probability wave of the electron is like a cloud, spreading throughout the entire atom, and the electron can appear everywhere at the same time.

Where it appears specifically depends on the value calculated from the wave function, namely |ψ|.

According to the Schrödinger equation, we only need to find the wave function of the electron at time t, and then the wave functions at all subsequent times can be found.

Third, although probability waves are not real waves, they can undergo interference, diffraction and other phenomena like real waves.

For example, when two electron waves come together, interference behavior may occur.

This interference is like a superposition of probabilities.

It can be said that no one present now dares to believe in the probability wave theory.

It's so scary!

Einstein murmured:

"impossible!"

"Absolutely impossible!"

"Doesn't this mean that God is playing dice?"

Do you understand?

I think what I wrote is very easy to understand.

High school level is enough to understand.


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(End of this chapter)