1900: A physics genius wandering around Europe

Chapter 517: The flaws of matrix mechanics! The pinnacle of wave-particle duality! Matter wave theory! Everything is a wave!
Heisenberg's matrix mechanics was like a flash of lightning that broke through the night sky, illuminating the fog of the old quantum theory.

Through this theory, we can naturally derive the empirical formula of the hydrogen atom spectrum, the splitting of light in the electromagnetic field and other phenomena.

When physicists studied matrix mechanics in depth, everyone was amazed:
"Heisenberg is a true genius!"

The other party not only created the matrix from scratch, but also perfectly combined the matrix and physics.

Astonishing!

Heisenberg became famous and became a well-known physicist of the time.

He was invited to give lectures at many universities and institutions to promote his theory of quantum mechanics.

However, his first stop was, of course, the Quantum Research Institute.

"Without Professor Bruce, there would be no Heisenberg today."

Heisenberg knew that his theory was very obscure and difficult to understand, and that he needed to learn unpopular mathematical knowledge such as matrices.

So, he likes to always emphasize the advantages of theory.

At this moment, facing Professor Bruce and his colleagues in the institute, he talked freely:

"The basis of matrix mechanics is the discontinuity of electrons, which is consistent with the essence of quantum concepts."

"And it recognizes the transition behavior of electrons."

"Matrix mechanics is derived from the old quantum theory and retains some of its concepts, but it also goes beyond the old quantum theory."

“It relies on our actual measurements of atomic behavior, rather than imagining it.”

Schrödinger, Irena and others were filled with emotion.

If power fascinates politicians, academic achievement fascinates scientists.

Heisenberg is now a completely different person than before!
No longer shy or reserved, I became calm and composed, and open and confident.

Even the language style of the speech has a high-end quality.

At this time, Heisenberg smiled and added:
"Of course, I admit that matrix mechanics is a bit abstract."

"Many people wrote to me to complain about why such a difficult form of mathematics was created."

"To this, I can only say: There is no way, this is the truth."

"And compared to Professor Bruce's Riemannian geometry in general relativity, I think matrices are pretty simple."

"At least after studying for a while, everyone can deduce it freely."

Everyone burst into sighs.

Obviously, they didn't believe Heisenberg's nonsense.

Using the opponent's matrix mechanics to calculate the orbit of the hydrogen atom is almost a death sentence.

It would be even more difficult to calculate the properties of a hydrogen molecule composed of two hydrogen atoms.

It would be impossible to figure it out in a week or two.

The physics community has long suffered from matrix mechanics.

Li Qiwei looked at Heisenberg, who was smiling, and said with a smile in his heart:

"Xiao Hai, try to smile a little longer now, or you won't be able to smile anymore soon."

At this time, Schrödinger, who had always been expressionless, asked:
"Heisenberg, how do you explain the problem of visualization mentioned by Professor Einstein?"

"Does your matrix mechanics eliminate the physical form of electrons?"

Wow!
Everyone looked at Schrödinger.

In everyone's mind, Schrödinger has always been the big brother of the institute.

Not only does he have extensive research interests and is well-versed in many fields, but he also has a good temper and is very helpful.

His friends all respect and love him.

But in recent times, everyone vaguely discovered that Brother Xue was a little different.

"I feel like he was inspired by Pauli and Heisenberg."

"You know, Brother Xue is the first member of our institute and has the most seniority."

"But now, he has been overtaken by a young talent. I guess he must be feeling bad."

"Alas, what a pity! Brother Xue is such a smart man, but he lacks a key inspiration."

Everyone was discussing in a low voice, and Schrödinger did not hear what was being said about him.

He did not ask questions specifically targeting Heisenberg.

Instead, he has made up his mind to specialize in quantum mechanics in the future.

As he grew older, Schrödinger worried that he would spend his whole life in mediocrity.

Therefore, he didn't want to waste his time on trial and error.

He wanted to choose a specific field and keep going deeper and deeper.

And quantum mechanics gave him the direction!

The birth of a new theory is bound to be full of opportunities.

If you don't seize the opportunity now, you will never have another chance in the future.

So, he is very concerned about matrix mechanics, especially its current problems.

If there are problems, it means there is room for optimization and improvement.

At this moment, Heisenberg didn't know what Schrödinger was thinking.

He was not upset by the question.

On the contrary, he also respected this senior in the institute.

Heisenberg was confident that his matrix mechanics could explain everything in quantum theory!
"Dr. Schrödinger, thank you for your question."

“I don’t think this is an issue that needs to be discussed.”

"I can find a contrasting example."

"That's Maxwell's equations."

"Electromagnetic waves, like atoms, are real physical entities."

"But using Maxwell's equations, can we imagine how electricity generates magnetism?"

"I'm not talking about the behavior of electromagnetic induction, but the principle behind it."

"I'm afraid not."

“So, I think matrix mechanics, it’s a little bit like Maxwell’s equations.”

"Through matrices, the behavior of atoms can be mathematically represented."

"Besides, at this stage we cannot observe the interior of an atom at all, and can only describe it through mathematical means."

"Therefore, I think the visualization problem of matrix mechanics is not a fatal problem."

“Of course, everything is a work in progress.”

"Perhaps matrix mechanics will be further improved in the future."

Schrodinger nodded slightly.

Although Heisenberg's answer did not convince him, he could not point out the specific errors in matrix mechanics.

No matter how abstract matrix mechanics is, at least it's useful.

This alone is enough to outweigh all other shortcomings.

Heisenberg glanced around confidently, hoping that someone would continue to ask questions.

Because every question is a perfection of his theory.

Just like the old quantum theory, there was only one quantum number when it was first proposed, but it eventually became four quantum numbers.

Heisenberg achieved success and reached the pinnacle of his life, but he was not so conceited as to think that his theory was perfect.

Even Professor Bruce wouldn't dare say such a thing.

Any physical theory will continue to evolve over time.

suddenly.

He noticed that there was something wrong with Professor Bruce's expression.

A little solemn, as if in deep thought.

At this time, everyone also noticed the abnormality and were very confused.

Did Professor Bruce discover something?
This is a bit incredible!
“Although Professor Bruce is not the first author of matrix mechanics, his contribution cannot be ignored.”

"This shows that he must have recognized matrix mechanics. Otherwise, how could he agree to publish it?"

"But what does this expression mean?"

Schrödinger's heart was beating fast.

He found it a little unbelievable.

Matrix mechanics was completed by Heisenberg under the guidance of Professor Bruce.

How could the other party possibly question it?

Under the gaze and confusion of everyone, Li Qiwei spoke.

"Heisenberg, you just said that the basis of matrix mechanics is the discontinuity of electrons."

“In fact, the discontinuity of electrons is the particle nature of electrons.”

"But you can think outside the box. What if electrons are not particles?"

"Can matrix mechanics still hold?"

Wow!
As soon as these words were spoken, the whole room fell silent.

Everyone's eyes widened in disbelief.

"Professor Bruce, would you mind looking at what you are saying?"

“Aren’t electrons particles?”

"Then what is it?"

Heisenberg was bewildered.

He even suspected that he had heard it wrongly.

Professor Bruce publicly spoke highly of matrix mechanics.

Call it the turning point when physics moves from darkness to light.

But now, the other party actually raised such a seemingly fantastic question based on the foundation of matrix mechanics.

For a moment, Heisenberg didn't know what to say.

At this time, Irena, as the only girl in the institute, spoke up to break the awkwardness.

"Professor, weren't you praising matrix mechanics earlier?"

"Why do you now think there is something wrong with the foundation of this theory?"

Everyone immediately pricked up their ears, they really wanted to know the reason.

Li Qiwei looked at Irena and said:

"I'm not questioning the correctness of matrix mechanics."

"As a reconstruction of the old quantum theory, it is very successful."

"There's no doubt about that."

"However, when I was using matrix mechanics, there was a phenomenon that I couldn't explain."

"That's the wave-particle duality of light!"

Wow!
Everyone was shocked!
Irena frowned slightly, with a puzzled look on her pretty face.

“Wave-particle duality?”

Ridgeway explained:

“The simple harmonic oscillator model used by Heisenberg is a model for moving matter.”

"In other words, it can't handle fluctuations like electromagnetic waves."

"We can explain the particle nature of light very well using matrix mechanics."

"But matrix mechanics can't do anything about its volatility."

Irena suddenly realized!
That's it!

Everyone was instantly impressed by Professor Bruce.

When others were still immersed in using matrix mechanics to explain atomic spectra, Professor Bruce actually thought of using it to study the wave-particle duality.

The most important thing is that we found an inexplicable problem!

"Professor Bruce is so scary!"

After hearing this, Schrödinger felt a huge wave of emotion in his heart!

He had just decided to devote his whole life to studying quantum mechanics when Professor Bruce provided him with a direction.

And it's a very imaginative direction.

Yes, photons are also microscopic particles, but unlike particles such as electrons, photons have the dual nature of wave and particle.

Matrix mechanics can deal with the particle nature of photons, but cannot deal with the wave nature of photons.

This shows that there is room for improvement in matrix mechanics.

This is great news for Schrödinger.

But for Heisenberg, it was terrible news.

He quickly retorted:

"Professor, I disagree with you."

"Matrix mechanics is based on the behavior of electrons."

"And the electron itself is a particle, not a wave."

"Matrix mechanics does not require properties that can handle waves."

"The wave nature of photons is a factor that needs to be considered separately." "So, your hypothesis is not valid."

Irena and the others nodded.

This time, no one stood on Professor Bruce's side, but instead all supported Heisenberg.

Because electrons are particles, this is simply common sense.

Since matrix mechanics can perfectly explain everything about electrons, there is no need to make major changes due to the wave nature of photons.

Schrödinger rubbed his chin with his right hand and thought quietly.

He subjectively supports Professor Bruce.

But objectively, he felt that what Heisenberg said did make sense.

After all, electrons and photons have different properties and cannot be confused.

In response to Heisenberg's reply, Li Qiwei smiled slightly.

He had already guessed that the other party would answer like this.

At this moment, he said quietly:
"What if electrons are not only particles, but also waves?"

boom!
Everyone was shocked!

Heisenberg was completely stunned.

"This"

"impossible."
-
Heisenberg regarded the sharing session at the Quantum Institute as a nightmare and chose to forget it.

He would never agree with Professor Bruce's point of view.

No matter how much he respects the other person.

Because the idea that electrons are waves is so horrifying!

It’s like a fantasy!
Not only him, but Irena and everyone else didn't believe it.

Besides, in the end, Professor Bruce just laughed it off and did not discuss it further.

This made everyone think that it was Professor Bruce who was brainstorming.

Anyway, in previous meetings, people have always raised all kinds of strange and bizarre ideas.

Therefore, Heisenberg didn't care.

He continued to give lectures at various universities and research institutes, explaining his matrix mechanics.

Meanwhile, in France, University of Paris.

After attending a meeting abroad, Lang Zhiwan immediately returned to his laboratory to continue his research.

Since the Marie Curie incident, he has devoted all his energy to the field of science.

People are much more mature than before.

As a contemporary of Professor Bruce, Lang Zhiwan was not very satisfied with his personal development.

He is a bit like Schrödinger, and his research field is very broad.

X-rays, gas theory, magnetic theory, relativity, quantum theory, etc. all have certain academic achievements.

But there is still a little distance to reach the top of physics.

It’s because he doesn’t have any important achievements.

However, his foundation is indeed solid, and he can be considered as one of the first-tier figures after the physics masters.

The students were very excited to see their mentor return.

They asked the most pressing questions:
"Professor, do you know quantum mechanics and matrix mechanics?"

Lang Zhiwan smiled and said:
"of course I know."

"Although I happened to be attending a meeting in the United States during that time."

“But the impact of this paper on the physics community is so huge.”

"I have read the paper several times."

Suddenly, Lang Zhiwan changed the subject and said with emotion:
"Hey, if only one of you could publish a paper like this."

"I would retire right now."

"We in France are lagging far behind in the field of modern physics."

Everyone looked at each other, too embarrassed to respond.

Of course they want to.

But everyone knows themselves.

What a genius Heisenberg is!
Not to mention these people, even the tutor himself can't compare to them.

Lang Zhiwan also felt that he was being a bit unreasonable.

So he changed the subject and asked:
"Where's de Broglie?"

"He still hasn't come to school recently?"

Someone replied:

"Mr. de Broglie hasn't been here for half a year."

Lang Zhiwan sighed and said nothing.

De Broglie's identity is too sensitive.

Even if he is the other party's mentor, it is impossible for him to be as strict as he treats ordinary students.

Therefore, he always let de Broglie do what he wanted.

Regarding research topics, try to follow the other person's wishes.

It’s just that he hasn’t been to school or the laboratory for such a long time.

Lang Zhiwan felt that de Broglie might not be able to continue his doctoral studies.

"No wonder, after all, he switched from history to physics."

"My foundation is so poor that I feel a little overwhelmed when I study the most cutting-edge fields now."

Lang Zhiwan even prepared for the worst.

If there was no other option, in order to save face for de Broglie's brother, he had to find a way to help him graduate successfully and get a doctorate degree.

After all, not every PhD needs to be as extraordinary as Bruce, Bohr and others.

At this moment, De Broglie, as Lang Zhiwan mentioned, has been secluded in his own mansion for half a year.

With two maids taking care of his daily life, de Broglie devoted all his time to research.

During this period, even when he learned that Heisenberg published matrix mechanics, he was not too surprised.

Because he knew that his results were absolutely perfect!
Now, he just needs the finishing touch.

In the study, de Broglie was writing furiously, his eyes extremely focused.

Bruce's shocking words from half a year ago came back to his mind:

“Since wave-like photons have particle properties, can particle-like electrons also have wave properties?”

His brother Maurice thought that electrons were waves, which was simply a fantasy.

He is a typical professional student, and he has learned concepts such as Newtonian mechanics, matter, motion, etc. since childhood.

Matter and waves are two distinct phenomena.

Although there is an elusive existence like photons.

But after all, photons travel at the speed of light, so some of their special properties are easy to understand.

But electronics are different!

It is a real substance, just like an apple or the earth.

How could such an existence be a wave?
This directly overturned Morris's decades-long scientific views.

This is unacceptable in any way.

But de Broglie did not have so many ideological burdens.

He switched from liberal arts to science, which allowed him to break free from the constraints of fixed thinking.

“Why can’t electrons be waves?”

He was fascinated by Professor Bruce's ideas.

However, opinions are just opinions. In order to form a paper, rigorous theoretical logical deduction is required.

And for more than half a year, de Broglie has been working hard for this goal.

He carefully reviewed the process by which Professor Bruce theoretically proved the wave-particle duality of light.

Got inspiration from it.

According to the mass-energy equation: E=mc.

According to the Lee-Planck formula in quantum theory: E=hv.

Based on these two formulas, de Broglie made a bold assumption:

Particles and waves have the same properties!
He believes that in the quantum world, the two can be seen as the same statement.

So, for electrons, we have:

mc=hv.

But there is a problem here.

After all, electrons are material particles and cannot move at the speed of light like photons.

Therefore, de Broglie needed to find a way to eliminate the physical quantity of the speed of light c.

Turn it into an ordinary wave relationship.

To do this, he replaced the speed of light with the product of the group velocity and the phase velocity.

Light is an electromagnetic wave, and group velocity and phase velocity are concepts in wave mechanics.

Just understand it briefly.

Assume that a waving curve is a sine curve.

Then the phase velocity refers to the propagation speed of the crest or trough, represented by u.

The group velocity refers to the propagation speed of a group of packets from 0 to 2π, represented by v (group).

After derivation, for electromagnetic waves such as light, the square of its wave velocity c=uv (group).

Therefore, the formula becomes: muv(group) = hv. (1)

According to the phase velocity divided by the wavelength, it is equal to the frequency, that is, v = u/λ, (2)

Combining (1) and (2) we can get:
λ = hu/muv (group) = h/mv (group). (3)

After getting here, there is still one final finishing touch.

That is how the group velocity is linked to the motion of the electron.

Group velocity is a property of waves, and the motion of electrons is a property of particles.

How to combine the two?
After thinking for half a year, de Broglie finally found the answer.

He once again made a bold assumption:

He believed that the wave and particle properties of electrons exist at the same time, and that electrons are like surfers, whose movement follows the waves.

(The waveguide theory is too complicated to be demonstrated)

Based on this assumption, the momentum and wave of the electron can be linked together.

Finally, we can conclude that momentum p = mv (group). (4)

Combining (3) and (4), de Broglie derived an incredible formula:

λ=h/p.

The wavelength of an electron, λ, is equal to the Lie-Planck constant divided by the momentum of the electron.

This shows that electrons do have wave properties.

The wave-particle duality is perfectly reflected in electrons!

De Broglie even went further and boldly speculated in his paper:
“The wave-particle duality is not limited to photons.”

“All microscopic particles, including electrons, protons, etc., have the dual nature of wave and particle.”

"Furthermore, macroscopic matter also has the wave-particle duality."

“Everything is in motion!”

boom!
De Broglie was even shocked by what he himself wrote!
Based on Professor Bruce's work, he not only deduced in detail and rigorously that electrons have the wave-particle duality.

Even according to his formula, it can be generalized that any substance exhibits wave properties.

De Broglie named this wave "matter wave".

It means the wave nature of matter itself!

At this moment, de Broglie was breathing rapidly and trembling all over.

That was an expression of extreme excitement.

His paper brought Professor Bruce's wave-particle duality of light to the pinnacle!
"call!"

After an unknown amount of time, de Broglie finally calmed down.

He stood up, walked to the window, looked at the sky and the earth outside, his heart clear.

At this moment, he was extremely grateful to Professor Bruce.

"Without Professor Bruce, there would be no matter waves, and there would be no de Broglie today."

He is the next heir to the Dukedom. His family's mansion has been passed down for hundreds of years and the family wealth is incalculable.

He is surrounded by beautiful women and all his contacts are high-ranking officials and dignitaries.

However, in de Broglie's view, all this is like a passing cloud.

How to relieve worries? Only physics!
"I came on the wave, and I will go on the wave."

boom!
The sound is ethereal and goes straight into the sky!
(End of this chapter)