1900: A physics genius wandering around Europe

Chapter 544: A Confrontation of the Ultimates! A New Explanation! The Meaning of the Formula! It Cannot Be Measured, and It Does Not Exist!

In later generations, the uncertainty principle is like the mass-energy equation. Since the formulas look very simple, anyone can say a few words about it.

However, most people do not have the corresponding knowledge reserves and are prone to making huge errors in their understanding of the formula.

It would be even worse if they read a few articles from low-quality popular science marketing accounts and were brainwashed, and they wouldn’t be able to change their thinking.

This cannot be blamed on everyone, because in real history, when Heisenberg proposed the uncertainty principle, his own understanding was wrong.
In the end, it was Bohr who gave the correct explanation.

You see, even the person who proposed the theory himself misunderstood it. You can imagine how difficult quantum mechanics is.

And now, when Ridgway first proposed the formula for the uncertainty principle, Heisenberg's fate was repeated.

His understanding, in fact, is the same as that of most people, and is also the understanding of those ordinary marketing accounts in later generations.

Heisenberg believed that in order to measure the position and momentum of an electron, it was necessary to collide with other particles or photons.

If you want to measure the position of an electron accurately, you have to use light with a shorter wavelength, because if the wavelength is too long, it will directly bypass the electron.

However, the shorter the wavelength of the photon, the greater its energy according to E=hv, so when it hits the electron, the greater the change in the electron's momentum will naturally be.

In summary, the operation of measuring the position of an electron using photons interferes with the momentum of the electron.

Therefore, we cannot accurately measure the position and velocity of an electron at the same time.

The above view of "measurement interference theory" is of course wrong.

The reason why it is popular is that it sounds very [easy to understand] and even middle school students can understand it.

But what is wrong is wrong, no matter how easy it is to understand.

The uncertainty principle is an inherent property of particles such as electrons and does not depend on any external measurement.

The explanation that Li Qiwei just gave based on Heisenberg is still a bit too complicated and has some minor flaws.

He planned to restate the uncertainty principle from another more fundamental perspective.

But at this moment, Dirac's voice sounded:
"Professor, I think your explanation is slightly wrong."

Wow!
It was as if a cold wind was blowing from the snow-capped mountains.

Everyone was shocked!
The lonely and silent Dirac always gives people the impression that he is a man who would make a big splash if he does not make a name for himself.

There was surprise in Rutherford and Fowler's eyes.

They valued Dirac much more than anyone else.

The other party may be Britain's only hope in the field of theoretical physics.

He is also known as the strongest genius of the era born in 1900!
And now, the debate between Dirac and Professor Bruce can be described as a collision between an unparalleled genius and an unparalleled strong man!

Everyone is looking forward to it.

At this time, Li Qiwei looked calm, and said with a smile in his heart: Classmate Xiao Di’s time has not yet come, but he can’t help but get restless.

So he smiled and said:

"Go ahead, Dr. Dirac."

Dirac said:
"Professor, you believe that the inability to accurately measure both the displacement and momentum of an electron is limited by the properties of the particle itself."

"But is there a possibility that, although we cannot measure it, it does not mean that the electron does not have a simultaneous definite momentum and displacement at a certain moment?"

“Just because it can’t be detected doesn’t mean it doesn’t exist?”

boom!
It was like a bomb exploding in everyone's ears.

Dirac's ideas shocked everyone.

Yup!

Being undetectable and existing are two completely different things.

According to Professor Bruce, the displacement and momentum of electrons have nothing to do with the measuring instrument or the measurement behavior.

It is inherently unmeasurable, just like why the speed of light has that value; they are all axiomatic phenomena.

However, this explanation only means that it cannot be measured, but it does not mean that the precise displacement and momentum of the electron do not exist.

Let me give you a vivid example.

You did something wrong and made your girlfriend angry.

Although you know your girlfriend is definitely angry, you can't tell from her expression.

Just because you can’t see it doesn’t mean it doesn’t exist!

The mysteriousness of women is comparable to quantum mechanics.

Everyone was talking about it.

“This logic seems to be correct.”

"I feel like Dirac's view seems to make more sense than Professor Bruce's?"

"And in this way, the uncertainty principle does not break determinism."

"It's just that some rules restrict our ability to measure particles precisely."

It is clear that most people are very supportive of Dirac.

He is indeed a peerless genius, and his every move is at a peak that ordinary people cannot reach.

He is actually able to overpower Professor Bruce!

Horror!
Heisenberg panicked instantly.

He found that he had no way of refuting Dirac.

This view hits home a bit, and is hard to disprove!

However, he still has the biggest backer.

"Professor Bruce will definitely be able to handle it!"

At this moment, everyone's eyes were focused on Li Qiwei.

He looked at Dirac and felt deeply moved.

This most low-key and powerful genius in quantum mechanics has finally begun to emerge.

The questioning angle is extremely sharp.

However, Li Qiwei remained calm and composed, and his dominance was unparalleled.

"Unfortunately, you are facing me!"

Amid the tense anticipation of the crowd, he spoke:
"First of all, I can say with certainty that Dirac was wrong."

"The uncertainty principle does more than just state that it is impossible to measure both the displacement and momentum of an electron accurately at the same time."

"At the same time, it also shows that the very thing [that electrons have precise displacement and momentum] does not exist!"

Everyone was shocked!

"Maybe I just used Heisenberg's example and caused misunderstanding."

"Your thinking is always limited to the act of [measurement]."

"So, I'm going to change the angle and re-explain the uncertainty principle."

"Now, please follow me and re-examine this formula: x·p≥h/4π."

"When Pauli questioned me before, he actually said something wrong, and I didn't correct him at the time."

"What's the concept?"

"That's what x and p stand for."

"Pauli said: x represents the change in displacement of the electron, and p represents the change in momentum of the electron."

“This statement is wrong.”

"The correct statement is: x represents the [standard deviation] of the electron's position, and p represents the standard deviation of the electron's momentum."

“Standard deviation and variation are not the same thing.”

"Most people look at an x ​​and subconsciously interpret it as a small change in position, and think it is caused by measurement error."

"This would lead to the kind of explanation that Heisenberg just proposed."

"But x actually represents the standard deviation of the position."

"It's my fault, I wrote it in a hurry."

"If the formula is written as: σx·σp≥h/4π, it may be less likely to cause misunderstanding."

Wow!
This difference in details surprised everyone.

Most people can’t even understand the derivation of the formula on the blackboard, so how can they understand the precise meaning of the formula?

All their understanding came from what Pauli had just said.

The standard deviation describes the degree to which each data in a set of data deviates from the mean value of the data.

比如现在有一组数：1、2、3、4、5。那么这组数的平均数就是3。

The standard deviation means how close the five numbers 12345 are to the mean of 5.

Obviously, only multiple data can produce the concept of standard deviation.

The change refers to the change before and after a number.

比如电子现在的动量是1，下一刻的动量是2，那么它的动量变化量就是2-1=1。

This is what Pauli thought p meant, but it is not.

At this time, Wilson was a little confused, and he asked directly:
"Bruce, there's a problem with this though."

"How can the position and momentum of an electron have a statistically significant standard deviation?"

"There is only one number for these two quantities, so there is no way they can have a standard deviation."

Everyone nodded when they heard this.

An object's position and momentum are both definite values.

There is no concept of standard deviation for a single number.

Li Qiwei heard this, smiled, and said calmly:

"Because of the existence of probability waves!"

"In classical mechanics, there is certainly no concept of standard deviation for position and momentum."

"Because they are a fixed number at any given time, they don't fluctuate, and there is no set number."

"For example, the momentum of a car is 1. At this moment, it is a definite number and has no statistical significance."

"But in quantum mechanics, things are different."

"According to probability wave theory, electrons can be everywhere inside an atom at the same time."

"Since it is simultaneous, the electron can be at point A, point B, or point C."

"The difference between the points is only the probability."

"Then that would produce a set of numbers."

"Since the electron can be either here or there, can't we calculate the average position of the electron?"

"With the average value, the fluctuation of each position of point ABC relative to the average value can also be calculated."

"This gives rise to the standard deviation σx of the electron's position."

"Similarly, based on the probability wave, we can also calculate the standard deviation of the electron's momentum, σp."

"In this way, we can discuss the standard deviation of the mechanical quantities of a single electron in a statistical sense."

"According to the derivation of matrix mechanics, the result is σx·σp≥h/4π."

“This is what the uncertainty principle really means!”

quiet!
Deathly silence!

Everyone was completely shocked by Li Qiwei's analysis!
It was not until now that they truly understood what was written on the blackboard.

"That Pauli guy misled me!"

Obviously, Pauli's previous explanation was completely misleading, which led to deviations in everyone's understanding.

However, you can't blame him.

Li Qiwei was only concerned with his own deductions at the time and did not explain loudly.

Pauli understood a lot of things based on his own feelings.

Mistakes are understandable.

And the shock brought by that formula was too great.

Li Qiwei didn't even have time to explain it in advance.

However, Pauli himself showed a rare look of shame.

After listening to Professor Bruce's explanation, he completely understood.

The uncertainty principle no longer holds any secrets for him.

He now completely agreed with this theory from the bottom of his heart.

He even knew how to answer Dirac.

The answer is already obvious.

Heisenberg looked shocked!
It seemed as if a huge wave was rising in his heart.

He had previously thought that he could fully understand the derivation on the blackboard.

Now it seems that he overestimated himself a bit.

Professor Bruce's explanation of the formula is perfect.

It is both easy to understand and rigorous and detailed.

Everyone on the field understood the true meaning of the uncertainty principle.

And most importantly, Professor Bruce combined probability waves and the uncertainty principle.

This is equivalent to combining wave mechanics and matrix mechanics together.

This is a crucial step!
Although Heisenberg hated wave mechanics, he knew deep down that the integration of the two was the only way forward.

Physics does not allow two contradictory theories to exist at the same time.

Although they are all correct, their physical meaning must be accommodated in a higher framework.

When that day comes, Heisenberg will be able to accept it.

But the prerequisite is that it must be completed by Professor Bruce.

If it were anyone else, he wouldn't accept it.

Heisenberg was once again impressed by Professor Bruce's terrifying strength!
At this time, Li Qiwei looked at Dirac and continued:

"Dirac, now I can answer your question."

"Based on the analysis just now, we know that σx and σp are properties of the electron that exist because of the probability wave."

“This standard deviation has nothing to do with whether you measure it or not.”

"Because even if you measure it, the electron still has the properties of a probability wave, and a probability wave is not affected by any factors."

"The position and momentum of an electron are inherently uncertain and governed by probability."

"So, the phenomenon you mentioned, 'although it cannot be measured, it exists', does not exist!"

"Theoretically, it doesn't exist!"

"Of course, if you don't acknowledge the probability wave, that's another matter."

"Also, this explanation makes it more clear why Heisenberg was wrong."

"Because σx and σp can be calculated before measurement, it has nothing to do with the measurement behavior."

"So how can a disturbance in the measurement introduce errors?"

"The essence of the uncertainty principle is that [determining the position and momentum of an electron at the same time] is something that cannot be measured and does not exist!"

boom!
Dirac was shocked when he heard this!
For the first time, a change of expression appeared on his face.

That is the feeling of awe in the face of an intelligence that completely surpasses one's own.

Professor Bruce is so powerful!
terrible!

There is no doubt that Professor Bruce completely convinced him.

He couldn't find any reason to refute it.

This peculiar property of electrons is indeed its inherent attribute.

Dirac himself agreed with probability waves, so of course he accepted Professor Bruce's latest explanation.

This is a logical deduction process that is linked together.

Dirac was completely convinced.

"Thank you, Professor Bruce, for answering my questions."

"I agree with your theoretical analysis."

Wow!
The whole audience was shocked!

Pauli and Dirac, two peerless geniuses, were successively conquered by Professor Bruce's extraordinary strength.

At this moment, no one questioned the uncertainty principle anymore.

(End of this chapter)