1900: A physics genius wandering around Europe

Chapter 547 Paper published! The academic community is shocked! Li Qiwei strikes again! Time-energy uncertainty relationship!
1924 3 Month 25 Day.

The paper on quantum tunneling effect was published in a German physics journal.

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

Professor Bruce's probability wave and uncertainty principle have been proven!
This is truly a ground-breaking event in the field of quantum mechanics.

Everyone was shocked!
"Oh! God! It turns out that our world is really so incredible!"

"There is neither causality nor determinism, but chaos!"

"Now philosophers have something to work with."

Probability waves and the uncertainty principle have overturned everyone's traditional cognition.

Human beings’ research on the nature of the world has entered a whole new realm.

Countless people shouted Bruce's name!

"Professor Bruce is so powerful!"

"Starting from the special theory of relativity, every physics theory he published was a revolutionary and groundbreaking theory."

"He represents the pinnacle of human wisdom!"

"So scary!"

For most people, Professor Bruce is too high and too far away, an existence that is beyond their reach.

Instead of pursuing unrealistic dreams, it is better to keep your feet on the ground and see how those tangible geniuses think and research.

As a result, Hund's name became famous in the physics community.

Only then did everyone realize that this low-key genius was actually the originator of Hund's rule.

But his previous fame was far less than that of Pauli and others.

Everyone sighed:

"The quantum world is coming!"

"In addition to those known peerless geniuses, the hidden strengths of many sects are also beginning to emerge."

For a time, the University of Göttingen became famous.

It has become a new holy land for quantum mechanics research after the Quantum Institute, the Institute of the University of Copenhagen, and the University of Berlin.

Many researchers and students come here to visit.

This put Fermi under considerable pressure.

He was a genius of the same generation as Heisenberg, Pauli, Dirac and others.

And now, many of the latter have made the leap to become physicists.

Although quantum mechanics is extremely brilliant, it is also a cruel arena of wisdom.

Genius is just an admission ticket!

Compared with Fermi, Dirac seemed calm and composed.

After arriving at the Quantum Research Institute, he suddenly felt like a fish in water.

Everything here makes him feel free.

He was obsessed with the study of quantum mechanics.

At this moment, Li Qiwei was discussing the quantum tunneling effect with Dirac.

He looked at the handsome young man in front of him and felt very satisfied.

This is a genius born for mathematics and physics!
The longer I spend with Dirac, the more I can feel the purity of him.

If Li Qiwei is the king of the scientific world, he not only has a love for science, but also shoulders important leadership responsibilities.

Then Dirac is the child picking up stones on the beach in this world.

In a sense, both are pure, but the artistic conception and level of purity are different.

Dirac's silence was due to his childhood experiences.

He always believed that his brother's suicide was caused by his father's betrayal of the family.

So, he became withdrawn from then on, unwilling to argue or even communicate with others.

Perhaps it was for this reason that he plunged headfirst into the ocean of science.

Science and truth will never betray or leave him.

However, under the subtle influence of Li Qiwei, Dirac became much more lively than before.

At this time, he suddenly said:

"Professor, I think Hund's explanation of the quantum tunneling effect using the conclusion of the uncertainty principle is a bit flawed."

Upon hearing this, Li Qiwei smiled slightly and asked:

"How to say?"

Dirac picked up a pen and paper and said as he calculated:
"Hund believed that it was the change in momentum that led to the change in kinetic energy, which enabled the molecule to pass through the barrier."

"However, he did not consider the effects of molecular potential energy."

"For microscopic particles, their total energy includes kinetic energy and potential energy."

“And the so-called obstacles are also potential energy barriers at the molecular level.”

"So, I think Hunt didn't consider it comprehensively enough."

"Of course, quantum tunneling itself is a very important experimental phenomenon."

“It’s a powerful demonstration of probability waves and the uncertainty principle!”

“But the details need to be optimized.”

“Can the uncertainty principle be considered from the perspective of total energy as a whole?”

After listening to Dirac's analysis, Li Qiwei was shocked.

As expected, as the big man behind quantum mechanics, Dirac had an extremely sharp vision.

There is nothing wrong with the quantum tunneling effect discovered by Hund.

The uncertainty principle is used to explain this phenomenon.

but.

In real history, the uncertainty principle has two equally important formulations.

Position-momentum uncertainty relation: x·p≥h/4π;

Time-energy uncertainty relation: t·E≥h/4π.

The latter is the real key to explaining the quantum tunneling effect!

In quantum mechanics, there is an important concept called conjugate quantity.

It refers to a pair of interrelated physical quantities in which a change in one quantity will cause a change in the other quantity.

Obviously, position and momentum are a pair of conjugate quantities.

Time and energy are also a pair of conjugate quantities.

Based on matrix mechanics, the uncertainty formulas for time and energy can also be derived.

Its form is the same as the position-momentum formula, but its connotation is slightly different.

At this time, Li Qiwei took out several manuscript papers from the drawer and handed them to Dirac.

"Look at it."

Dirac was confused as he had just been immersed in thinking about the quantum tunneling effect.

However, what Professor Bruce taught was definitely extraordinary.

He took the manuscript with both hands and began to read it carefully.

Just a few minutes later.

hiss!
Even with Dirac's extraordinary talent, he couldn't help but be shocked.

"Conjugate quantity!"

"The Time-Energy Uncertainty Principle!"

"t·E≥h/4π!"

Dirac had recently devoted a lot of effort to matrix mechanics, and he quickly understood the entire derivation process.

He couldn't help but exclaimed:
"It turns out that Professor Bruce has already seen through Hunt's problem."

“And you gave me a solution!”

"The real reason for quantum tunneling is time-energy uncertainty."

"The energy of microscopic particles can change dramatically in a very short period of time."

"So, at some point the energy of the molecule will exceed the potential energy barrier and pass through it!"

Dirac couldn't help but get excited.

This new formula perfectly explains the quantum tunneling effect.

It is not limited to kinetic energy, but considers the energy of the particle as a whole.

It coincides with his previous idea.

For a moment, Dirac felt an indescribable joy in his heart.

Not only was Professor Bruce thinking ahead of him about what he was thinking about, but he also solved it. His thinking was in sync with Professor Bruce's!

"Professor, you are so strong!"

At this moment, he no longer had the temperament of an iceberg snow lotus, but turned into a little fanboy.

In the face of Dirac's flattery, Li Qiwei smiled slightly.

"This formula is derived from the uncertainty in position-momentum."

"It's not difficult in itself. The important thing is to refine the concept of conjugate quantity."

Dirac listened silently. In front of Professor Bruce, he returned to his naive student days.

“And the time-energy relationship is a little different from the position-momentum relationship.”

"Can you tell the difference?"

Upon hearing this, Dirac's face turned serious.

Obviously, Professor Bruce was testing him.

He carefully studied the derivation on the manuscript again.

At the same time, his mind was still recalling the process of deriving the position-momentum formula.

Soon, Dirac frowned slightly and found the problem.

"In the formula x·p≥h/4π, x and p do not represent the amount of change, but the standard deviation."

"Then the same should be true for the formula t·E≥h/4π."

"E stands for the standard deviation of the particle energies."

“That’s easier to understand.”

"Energy is a mechanical quantity similar to position and momentum."

"Because of the probability wave, the energy of microscopic particles must also be fluctuating."

"So energy also has its own standard deviation."

"But how do we understand t, the standard deviation of time?"

Li Qiwei nodded, very satisfied.

Dirac saw the problem immediately.

"Time is not a mechanical quantity like energy; it is just a parameter."

“We can measure the position, momentum and other mechanical quantities of a particle at any moment, but it is impossible to measure the [time] of a particle.”

"Every mechanical quantity is a function of time."

"But particles don't have a mechanical quantity called [time] that changes with time."

“So, there is an essential difference between time and energy.”

"It is impossible for time to fluctuate due to probability waves, so there is no so-called standard deviation."

"Professor, I think the key point of this formula lies in the explanation of t!"

Li Qiwei laughed and praised:
"Dirac, there are rumors that you are the first genius of the new generation. It seems that your reputation is well-deserved."

Dirac blushed when he heard this.

In front of Professor Bruce, no one has the courage to call himself a genius, especially the number one genius.

At this time, Li Qiwei smiled and said:

"Your analysis is correct."

"With your ability, you should be able to figure out the explanation of T after a few more hours of study."

"I'll just tell you directly."

"Assuming that E = 0, it means that the energy of the particle no longer changes at this moment and becomes a [steady state]."

"Then t will go to infinity."

"What amount of time would be infinite?"

"That can only be the changing cycle of energy!"

"At this moment, the energy is fixed, which means it will never change, so its changing cycle is naturally infinite."

"So, t does not refer to the standard deviation of time, but to the period T of change of the average value of each mechanical quantity."

"For example, the average energy of a particle changes once every 2 seconds, from x joules to y joules."

"Then let's say the t of energy is 2 seconds."

"Now look back at the formula."

"When the average energy change period of a particle is very small, that is, t is very small, it means that the energy of the particle changes once in a very short time interval."

"And because t is very small, E is very large, so the energy value of the particle will vary over a very large range."

"Suppose t is one ten-millionth of a second."

"Perhaps the energy of a particle is 10 joules at one ten-millionth of a second, but becomes million joules at two ten-millionths of a second."

"At three ten-millionths of a second, it becomes 0.00001 joules."

"So the uncertainty in the energy of the particle is very, very large."

"This is the essence of the quantum tunneling effect."

"Due to probability, there will always be a time when the energy of a molecule exceeds the barrier and it will pass through it."

Wow!
Dirac suddenly realized!
It turns out that the time-energy uncertainty relationship can be understood in this way.

The faster the state of a particle changes, the greater the uncertainty of its mechanical quantities.

To put it in a more vivid way: the faster you draw the lottery, the greater the probability of winning!
Of course, lottery can even prevent time travel, so how can quantum mechanics break through its barriers?

At this point, Dirac had fully understood the uncertainty principle.

The magic of this theory is beyond imagination.

Many incredible concepts can be derived through the uncertainty principle.

One of the most famous concepts is the famous "quantum vacuum fluctuation"!
Closely related to it is an even more famous concept: vacuum zero-point energy.

The vacuum is not empty!

Creation of the void!

Human cognition has been subverted once again!

Li Qiwei suddenly smiled.

He has accepted Schrödinger's invitation to visit the University of Berlin in June and give a speech.

"When you give a speech, there should always be some surprises."

Pretending is like the wind, always with me!
-
1924 4 Month 10 Day.

Ridgwell published a supplementary paper on the time-energy uncertainty relation in the journal Nature.

As soon as the paper came out, the physics community was shocked!

This article not only improves the uncertainty principle, but also perfectly explains the quantum tunneling effect.

"My God!"

“Professor Bruce’s inspiration is simply endless!”

University of Göttingen.

After reading the paper, Hund and Fermi could not help but exclaim:
"Professor Bruce is so strong!"

“The uncertainty principle actually has a second formula!”

Born laughed bitterly and said self-deprecatingly:
"I'm kind of embarrassed now."

“I didn’t expect my explanation was wrong.”

Hunt comforted:
"Professor, you are too modest."

"Without your answer, perhaps Professor Bruce would not have figured out the time-energy uncertainty relationship."

"You have once again inspired Professor Bruce."

Born laughed.

University of Leipzig.

Although Heisenberg was already a professor-level figure.

But his character didn't become much calmer.

The quantum tunneling effect and the uncertainty principle made his matrix mechanics shine again.

Heisenberg was cheerful even when he was teaching his students.

"Students, matrix mechanics is the future of quantum mechanics!"

"From today on, I will lead everyone to learn about the matrix."

The students wailed.

At this point, the correctness of probability waves and the uncertainty principle has been supported by the vast majority of people!
Quantum mechanics has become a great theory that can truly rival the theory of relativity!

Research on it is unprecedentedly vigorous, with papers being published in large numbers.

(End of this chapter)