1900: A physics genius wandering around Europe

Chapter 559: A stroke of genius! Bruce's equation! Unifying special relativity and quantum mechanics! Shocking!
Inside the Technical University of Berlin.

Everyone understood the second problem of wave mechanics.

For those present, the calculation form of wave mechanics was still very simple.

At least it's not a big problem to understand.

However, everyone was deeply shocked.

There is actually a contradiction between quantum mechanics and relativity hidden in the problem.

This is truly a huge thing in the field of physics!

Must be solved!

At this moment, the projector is turned on.

Amid everyone's shock and expectation, Li Qiwei began his solution.

"Everyone, please look at this equation again: E=pc+mc."

“I did some transformations on it.”

"First, divide both sides of the equation by c, so it becomes: E/c=p+mc."

"Then, take the square root of both sides and you get: E/c=√(p+mc)."③
Everyone was very confused after seeing this.

“Isn’t this any different from just now?”

The previous formula ② is E=√(pc+mc).

Now it is equivalent to dividing both sides by c, which becomes Professor Bruce's formula ③.

But this still cannot solve the contradiction that Schrödinger encountered.

However, no one questioned it out loud.

Obviously, Professor Bruce must know this.

At this time, Li Qiwei raised his voice and his eyes became sharp.

"Pay attention, the most critical part is coming!"

Everyone seemed to have returned to their youth as students listening to their teacher's lectures.

"At this point, I let p+mc=(αp+βmc)."

"Then, formula ③ can be written as: E/c=αp+βmc."

"See, this way we can eliminate the square root without using the square, which solves the problem perfectly."

Wow!
Everyone was shocked!
Could it be that the problem that had troubled Schrödinger and others for a whole year was solved so easily?

This is incredible!
"My goodness!"

"This is so simple, I feel like I can figure it out."

“Why couldn’t a genius like Schrödinger think of this?”

"There must be something wrong here."

"."

Everyone was talking about it.

Schrödinger in the audience frowned slightly. He felt that there was something wrong with Professor Bruce's conversion.

If it were really that simple, just using α and β instead of squares, he might as well just run into a wall and die.

Suddenly, he thought of the problem.

"Professor, this conversion does eliminate the square root."

"But in your equation, do α and β really exist?"

At this time, Schrödinger stood up, he had thought it through completely.

"Let me explain it to you in a vivid way."

"Professor Bruce's idea is equivalent to solving [x+y=(Ax+By)]."

"Expanding the right side of the equation yields: x+y=Ax+By+2ABxy."

"Obviously, if you want this equation to hold."

"Then it must be: A=B=1, and AB=0."

"But how is this possible?"

"So, I think there's something wrong with Professor Bruce's conversion."

Wow!
The venue immediately became noisy.

Everyone understood Schrödinger's example immediately, without him even having to write it out.

Obviously, such A and B cannot exist.

AB has no real solutions at all, not even complex solutions.

That is, there is something wrong with this conversion.

In other words, Professor Bruce's alpha and beta do not exist at all!

Since it doesn't exist, there is no point in eliminating the square root.

Because that is just a formal elimination, and it is an equation that has no solution at all.

At this moment, everyone looked at Professor Bruce again. How would he explain Schrödinger's rebuttal?
Facing Schrödinger's doubts, Li Qiwei smiled slightly.

"Yes, Schrödinger's example is very good."

“It perfectly illustrates the problem with derivation.”

Suddenly, he exuded a domineering aura, shocking the whole audience.

"However, you can't solve it, but I can!"

boom!
The whole audience was shocked!

Everyone is in disbelief!
Even a middle school student can see the contradiction in this equation.

How could there be a solution?
How can A be both 1 and zero?

"Impossible! Absolutely impossible!"

Then, Li Qiwei said:
"First of all, there is nothing wrong with Schrödinger's expansion."

“But there is one area where I think it could be slightly modified.”

"Everyone, please look at the screen."

"x+y=Ax+By+2ABxy. This is Schrödinger's equation."

"Now, I rewrite it as: x+y=Ax+By+(AB+BA)xy."

Everyone was even more puzzled.

What is the additional meaning of writing 2AB separately as AB+BA?
Ridgeway continued:

"At this point, AB+BA=0, but what happens if we also assume that AB≠BA?"

"That's right!"

"The equation is now valid!"

"So, we just need to find the values ​​of A and B that meet the above conditions."

Wow!
Everyone was completely confused!
Everyone's face was filled with confusion.

"What?"

"Who can tell me what's going on?"

"How can AB not be equal to BA?"

"Isn't this nonsense?"

The meeting room suddenly became noisy, with people whispering to each other, unable to figure out the problem.

Not only AB+BA=0, but AB≠BA. How is this possible?
Even Planck, Einstein and other great men were confused.

They intuitively felt that this change must have a deeper meaning.

But this is too deep.

Is there really a number that satisfies A and B?

Schrödinger looked at the derivation on the screen and felt that he did not have enough brain cells.

Professor Bruce's ideas are so bizarre.

However, Heisenberg's eyes became brighter and brighter, and he felt that the thing in front of him was very familiar, very familiar.

"Oh my god!"

"Could it be that?"

At this time, Li Qiwei looked at everyone and suddenly smiled.

His words shocked the whole audience!

"Hasn't everyone figured it out yet?"

"A times B is not equal to B times A. Isn't that a matrix?"

"Heisenberg's matrix mechanics was proposed because of the discovery of this phenomenon."

"That's right, if A and B are not numbers but matrices, then everything makes sense!"

"And, indeed, such A-matrix and B-matrix exist."

“A=[0 1] B=[1 0]
[1 0][0 -1]”

"A and B are both 2×2 matrices."

“They satisfy AB+BA=0, and AB≠BA.”

quiet!
Deathly silence!

Everyone was shocked by this "stroke of genius".

Matrix is ​​introduced into wave mechanics!

What a fantastic and brilliant idea!

"Oh! God!"

"Professor Bruce is amazing!"

"We all thought that AB was a specific number, but Professor Bruce actually thought of them as matrices!"

"That's awesome!"

“Too cool!”

There was a burst of exclamations in the meeting hall.

Everyone was full of admiration!
A brilliant light burst out from Heisenberg's eyes.

"Sure enough!"

"It's really the Matrix!"

“Professor Bruce applied the core of matrix mechanics to wave mechanics.”

"Hahaha~"

"My matrix mechanics is the orthodoxy of quantum mechanics!"

"Wave mechanics needs to be perfected by matrix mechanics!"

"I wonder if anyone will dare to say that Matrix Mechanics is bad in the future."

At this moment, Heisenberg was in high spirits and very happy.

In Professor Bruce's hands, matrix mechanics is so amazing that it seems to be able to explain everything in the world.

Schrödinger was stunned and couldn't believe it!

In his wave mechanics, matrices actually appeared.

And only matrices can explain the problems in his equations.

Schrödinger was both happy and sad, it was just like a dream.

The good news is that the defects of wave mechanics have been solved.

Sadly, it was solved by matrix mechanics.

He sighed.

"Well, that's a good thing."

At this time, Li Qiwei continued:

"After solving this most critical problem, the following content will be easy to deduce."

"Now let's get back to the question."

"Since Schrödinger's wave equation is three-dimensional, the momentum p has three components xyz."

"Add MC, and you'll need four unknowns in total."

"So, we need to introduce a 4×4 matrix."

"The derivation of the matrix is ​​as follows:"

Swish!
Swish! !

Swish! ! !
~~~
Li Qiwei wrote with divine power, dazzling everyone present.

The complex matrix is ​​like a butcher cutting up an ox in his hands.

No one dared to blink or be distracted, because if they delayed for even a second, they might not be able to understand the next step.

Thirty minutes later, Li Qiwei finally stopped writing.

"Everyone, please take a look."

"This is my modified wave equation."

"Compared to Schrödinger's version, this equation can accurately describe the state of electrons moving at close to the speed of light."

"At this point, someone might wonder: What about the electron spin?"

"Haha." Li Qiwei smiled slightly.

"Don't forget that the advantage of matrix mechanics over wave mechanics is that it can explain electron spin."

"Because if you want to describe spin, you have to introduce matrices."

"And now, this new wave equation also includes matrices, so it can naturally describe spin."

(Why matrices can describe spins is a complex mathematical concept and will not be introduced here.)
"Just make the following transformations."

Swish!
Swish!

Swish swish!
After another round of operations, the new wave equation is finally simplified into a special form.

“That’s spin!”

call!
Li Qiwei took a deep breath.

Finally done.

The above content is the famous Dirac equation.

It is the relativistic form of the Schrödinger equation.

In real history, Dirac proposed the Dirac equation just one year after attending the fifth Solvay Conference.

When the paper came out, the world was shocked!

The entire physics community was shocked by this equation!
Because it unifies quantum mechanics and special relativity, it is simply astonishing.

Of course, it has an even more shocking corollary: positrons. This is Dirac, the first genius of quantum mechanics!

He is not well-known because he is too low-key, never shows off, and only likes to study mathematics and physics alone.

But in this life, it should be called "Bruce Equation".

Li Qiwei could only comfort Dirac silently in his heart.

"Xiao Di! Uncle Li won't take your things for nothing. I'll treat you to a big meal when I get back."

At this moment, everyone was stunned!

They could never have imagined that what Professor Bruce said was such an amazing theory.

It’s too shocking!

"My God!"

"too exaggerated!"

"Professor Bruce is so powerful!"

"He has unified quantum mechanics and special relativity!"

“It’s an achievement that makes people worship just thinking about it.”

"He created two completely different theories and now he's trying to unify them."

"This is the boss. He can do whatever he wants in the field of physics."

Schrödinger's scalp tingled!
His heart was in turmoil.

The derivation process on the screen was engraved into his mind bit by bit.

“So that’s how it is”

"No wonder I can't explain spin no matter what I try."

“Wave mechanics and matrix mechanics have never been independent of each other, but should draw on each other.”

Schrödinger is much more generous than Heisenberg in this respect.

He did not reject matrix mechanics, and anyone could learn it as long as it was helpful to his theory.

But he really couldn't think of such a wonderful idea.

Professor Bruce used a fanciful way of thinking to sew the matrix into wave mechanics.

Schrödinger now had some understanding of why it was useless even though he had consulted mathematicians.

Because this new wave equation requires not only mathematical skills but also physical thinking.

The two are combined into one, neither of them can be missing!

Schrödinger had physical ideas, but he was not familiar with matrices and could not think of this kind of transformation.

The mathematicians he found knew about matrices, but they had no physical thinking and did not know how to think about this kind of transformation.

Therefore, only Professor Bruce, who is proficient in both mathematics and physics, can break through this barrier and open up new horizons.

Einstein looked excited.

He smelled a hint of unity from Bruce's deduction.

This is the feat he has always dreamed of!

Once upon a time, Einstein was stubborn and wanted to unify gravity and electromagnetic force, but unfortunately he failed.

Later, the proposal of strong force and weak force forced him to give up.

After all, there are now four fundamental forces in nature instead of two, and his way of unification is problematic.

But now, Bruce showed him a new way to unify.

That is to unify quantum mechanics and relativity.

Although it only unified the special theory of relativity, it was still shocking enough.

He said to Planck beside him with great confidence:
"I estimate that in a few years, Bruce should be able to integrate general relativity with quantum mechanics."

Planck smiled and said:

"According to his development trend, I think it is very likely."

However, what the two bigwigs could not have imagined was that in real history, such a unified theory had not been completed for a hundred years.

Quantum mechanics is very compatible with special relativity, but it is completely incompatible with general relativity.

It's all because of gravity.

Quantum field theory quantizes everything in the world, except gravity.

This is the core contradiction between quantum mechanics and general relativity.

Among the speculations on this issue, there is one that later generations have come up with that is so imaginative that it can be said to be out of this world.

in turn!
What does that mean?

It’s not about quantizing gravity, but about [gravitating] the other three forces!
This conjecture holds that there is actually only one fundamental force in the universe, and that is gravity.

The other three forces are just changing forms of gravity under special space-time rules.

I have to say that this conjecture is indeed extremely bold and innovative enough.

Of course, there has been no progress yet.

At this moment, Ridgway initially unified quantum mechanics and special relativity, allowing Einstein and other great men to see the dawn of unification.

In the corner of the back row, Li Chengdao was so shocked that he was speechless.

"Second brother is right again!"

“It actually really introduced the Matrix!”

"This"

Li Chengdao really couldn't think of any words to describe his second brother.

Astonishing!

In his speech three days ago, Li Chengde also made correct predictions.

But that speech didn't require much math and physics.

It mainly tests your imagination.

But today's content is different.

Looking at the densely packed deductions on the screen, Li Chengdao felt like he was reading a book from heaven.

As for Li Chengde, it goes without saying.

However, the other party can still grasp the most important things with his strong intuition.

"Since matrices can prove spin, why not just use the matrix method?"

Li Chengde’s idea is so simple, but it hits the nail on the head!
Li Chengdao sighed:

"Second brother, listen to me and study physics in the future."

Li Chengde looked indifferent.

"Oh, brother, I haven't had enough fun yet."

"I plan to learn some music first to attract girls."

“When I see through the mundane world and see nothing but white people and skeletons, I will enter the realm of physics and pursue the path of truth.”

Li Chengdao:
At this moment, the atmosphere in the venue completely exploded.

Even if the many bigwigs present did not understand quantum mechanics, they could at least understand the ideas and processes of the derivation.

The new wave equation is more important than the previous quantum vacuum fluctuations.

The former is a theory that has been derived from actual experience, while the latter is just a conjecture.

Moreover, the new wave equation solves two difficult problems in wave mechanics and improves its foundation.

At this point, both versions of quantum mechanics are perfect.

From any one of them one can deduce everything about the old quantum theory.

Quantum mechanics has been accomplished!
However, quantum giants such as Schrödinger, Heisenberg, Pauli, Einstein, and Planck knew it.

There is one last crucial question left in quantum mechanics.

That is the deconstruction of wave-particle duality!

This is also a legacy of the last quantum mechanics conference.

Wave mechanics and matrix mechanics are now flawless.

But the deep contradictions between them have not yet been resolved.

Electrons and photons can be both waves and particles.

So the question is coming?

When do they behave as waves and when do they behave as particles?

What factors affect whether they become waves or particles?

A lot of experimental evidence has shown that electrons either behave as waves, such as electron diffraction, or as particles, such as collision experiments.

The phenomenon that electrons are both waves and particles at the same time has not yet been discovered or understood.

So which variable is giving "instructions" to the electrons?

It is impossible for electrons to have self-awareness.

"Oh, now I'm going to waver."

"Hey, I should appear as a particle in the next second."

Photons had the same problem in the past, but quantum mechanics had not yet been developed at that time, so it naturally could not be explained.

But now that quantum mechanics is mature enough, this problem must be solved.

Quantum mechanics must unify particles and waves.

In real history, the complementarity principle proposed by Bohr solved the above problems.

A complete description of a single quantum object must include both wave and particle properties.

And all of this will be revealed at the 4th Bruce Conference!

Now, Li Qiwei looked at everyone and continued:
"Based on the new wave equation, we can draw a conclusion."

"That is: electron spin is an inevitable requirement of the special theory of relativity!"

"Spin is a physical quantity used to describe the magnetic moment of an electron."

"It is an intrinsic property of the electron, just like mass, charge, etc."

"It's not the behavior we imagined electrons to be."

Everyone nodded after hearing this.

The concept of electron spin was indeed questioned when it was first proposed.

Because it really seems like it was forced together.

At that time, research on the fourth quantum number was in full swing.

Many physicists are looking for traces of it.

In the end, Uhlenbeck and his two men got there first.

They discovered spin.

But no one can explain the origin and mechanism of spin.

Even Professor Bruce at that time couldn't do it.

And today, the mystery of spin has finally been solved.

At this moment, everyone was in a good mood.

Professor Bruce never disappoints.

Once the content of today's meeting is made public, it will surely cause a huge earthquake in the physics community.

Moderator G. Hertz is ready to go on stage to summarize and start the next discussion session.

However, after he took a few steps, he realized something was wrong.

"Why hasn't Professor Bruce moved yet?"

"Hasn't he finished his theory?"

G. Hertz was a little confused.

"What's happening here?"

Soon, everyone present noticed this anomaly.

Under their surprised gaze, Professor Bruce raised his head, turned his back, and stared at the projection screen in front of him, as if thinking about something.

Wow!
The venue fell silent!
Everyone held their breath, not daring to disturb Professor Bruce's thoughts.

"Ah? What's going on? Is there something wrong with this new wave equation?"

"That's impossible. There are so many quantum mechanics experts here. If there really is a problem, it should have been discovered long ago."

"So what is Professor Bruce looking at?"

"do not know"

Heisenberg stared at the formula and read it carefully several times.

He was sure that there was absolutely no problem with Professor Bruce's deduction.

So, he was also very curious.

"Brother, what do you think Professor Bruce is looking at?"
When Pauli heard this, his sharp eyes moved back and forth.

He thought Professor Bruce must have discovered something strange.

"Could it be that the new equation is still incompatible?"

"impossible!"

"I can't figure it out."

Pauli shook his head.

Planck, Einstein and others looked at each other, all confused.

No one knows what happened.

One minute
five minutes.
Everyone had great trust in Professor Bruce, so they discussed in a low voice and did not dare to make loud noises to disturb him.

After a full ten minutes, Li Qiwei finally spoke.

He murmured to himself:
"I see."

Then, Li Qiwei came to his senses and smiled brightly at everyone.

"Sorry, everyone. I was lost in thought."

"Because I found a strange phenomenon in the new wave equation."

"Maybe I should tell you."

"This could overturn the current understanding of matter in physics."

Wow!
The whole audience was shocked!

Subverting the perception of matter?

How to subvert?

(End of this chapter)