40: Chapter 40 An Anatomy Through a Screen

Back at his home, the moment he took off his down jacket, Jiang Lin impatiently walked over to the sofa and reached out his hand toward his father, who was just sitting down to drink some water.

"Dad, lend me your phone for a bit."

"Take it, but don't play too long, it's bad for your eyes."

Jiang Jianguo cheerfully handed his slightly scratched smartphone to his son.

In the past, he might have nagged a couple of words about whether he was going to play games, but now, he had an almost blind trust in Jiang Lin.

Jiang Lin took the phone back to his bedroom, sat down in front of the desk, opened Douyin, typed "Quantum Mechanics Isn't That Mystical" into the search box, and found that Physics teacher's account.

He opened the works list and switched the sorting method from earliest to latest.

The earliest video was published more than a year ago.

The title was: [Why Is Quantum Mechanics So Hard?]

Professor Lu Zhixing in the video was wearing a loose gray sweater, sitting in that unchanging office.

On the whiteboard behind him, four large characters were written with a black marker: The Price of Intuition.

"Many students, and even some graduate students who have already been admitted to the Physics Department, will madly feel that Quantum Mechanics is too difficult in some late night. They always complain that it's because mathematical tools like wave functions, Hilbert spaces, and operator partial differential equations are too anti-human."

Speaking up to here, Professor Lu Zhixing raised a finger.

"These words are only half right."

"Mathematics is indeed difficult, there is no doubt about that. However, mathematics has never been the most painful part of learning Physics. Because mathematics is like a knife; no matter how dull the knife is, as long as you spend time sharpening it, you can always sharpen it and master how to use it."

"What truly makes people feel painful about learning Quantum Mechanics is that it forcefully demands you to give up the classical intuition that you have established in your subconscious since birth, since the moment you threw your first stone and observed the first apple fall, which you use to understand this macroscopic world."

Professor Lu Zhixing in the image leaned forward, his gaze piercing through the screen and striking straight into people's hearts.

"For a person to give up the intuition they rely on for survival is no different from reshaping their worldview, and that is extremely painful."

Jiang Lin deeply agreed with this.

Holding strong expectations, he continued to watch the second video.

The title was: [Understanding the Formulation Doesn't Mean Understanding the Concept — Beware of Intuition's Counter-Attack]

Professor Lu Zhixing said in the video: "I have seen many students who can score over ninety points on their final exams. If you ask them to write down the mathematical definition of quantum superposition states from memory, they can recite the Schrödinger equation word for word, and even proficiently write out the linear combination formula of state vectors."

Professor Lu Zhixing tapped on the formula on the whiteboard.

"However, does this mean he understands it? No, if you casually change him to a slightly variant physical scenario, you will find that in his subconscious, he will still stealthily think of the superposition of quantum states as some kind of ignorance of classical probability."

"For example, he will think that Schrödinger's cat is actually already dead or already alive before we open the box, and it's just that we don't know yet. He treats quantum superposition as classical probability caused by our insufficient information."

"The most terrifying thing is that the students themselves are completely unaware that they are making mistakes. Because this kind of error does not happen in black-and-white derivation operations, but in the gaps of intuition that they cannot even perceive themselves."

Jiang Lin pressed pause.

A page from his Wasteland concept notebook surfaced in his mind.

On that page, he had once drawn a picture with a pencil and written an analogy that he was quite proud of back then.

The sprouting seed.

He had once tried to use a seed buried in the soil that hadn't yet broken through the ground to analogize the quantum superposition state.

A seed is in the soil; it might grow roots to the left, or it might grow them to the right. Before it breaks through the ground and is observed, it seems to retain several possibilities of going both left and right simultaneously in the mud. Until the very last moment, you don't know which path it chooses.

This vitality-filled analogy, he used for a full two years.

During these two years, he used this model to understand the penetration of a one-dimensional potential barrier, even feeling extremely smooth, and fancied himself as having grasped the essence of Quantum Mechanics.

Until later.

Until he began to deal with phase and quantum interference in the remnant pages of a more advanced textbook.

When the superposition of two quantum states involved not only the addition and subtraction of probability amplitudes, but also the phase angles in the complex plane, quantum probabilities produced interference terms that could not be eliminated.

At that moment, that perfect seed analogy shattered into a ground full of powder.

Seeds could not produce interference. Because classical probability is P = P_1 + P_2, which is pure addition.

Whereas Quantum Mechanics is the superposition of wave functions, which possesses interference effects.

The roots on the left and the roots on the right could not cancel each other out to become no roots.

Afterwards, he drew a big cross over that seed in his concept notebook.

That was the first time he realized how painful the price would be of forcibly using macroscopic concreteness to analogize microscopic quanta.

As his thoughts reached here, he resumed playing the video.

Not just because this video gave him some unreachable new knowledge.

But because Professor Lu Zhixing, as a stranger far away at the edge of the horizon, had extremely calmly and accurately dissected the detours he once walked in the darkness and the pits he once fell into, making them crystal clear.

This cross-spatiotemporal understanding made him feel a huge shock.

The second series was a complete analysis of the double-slit experiment.

The first video only talked about the phenomenon.

Electrons were fired one by one.

Interference fringes finally formed on the screen.

Professor Lu Zhixing was not in a hurry to explain.

He said: "Let's not rush for the answers first."

"Many people are too hasty in learning Physics; before they can even see the phenomenon clearly, they want to stuff it into their own familiar framework."

Jiang Lin replayed this sentence once.

It and Jiang Yao's problem were like the same thing.

First ask clearly what the question is asking, and first see clearly what the phenomenon is.

The third video was the one his cousin scrolled across during the day.

The Observer Effect.

Jiang Lin watched again.

This time there was no television sound from his grandmother's house, no spatula sound from the kitchen, nor Zhang Yu's impatient fingers.

The bedroom was very quiet.

He listened to that sentence he had already heard once more.

"You think you are asking which slit the electron went through."

"But you are actually asking whether the matter of which slit it went through has any meaning when no measurement takes place."

Jiang Lin dragged the video back fifteen seconds.

He listened to it again, dragged it back, and listened a third time.

Only then did he put down his phone, pick up his pen, and write on the draft paper.

[It's not asking for the answer, but whether the question itself has a definition.]

After writing, he drew a very small square next to it.

This was not the answer.

But this was the shape of a better question.

He continued to watch downward.

The third series was Heisenberg's Uncertainty Principle.

Among them, the first video talked about the relationship between position and momentum.

Professor Lu Zhixing's expression was extremely rigorous and cautious; on short-video platforms that pursued instant gratification and gimmicks, he was simply a breath of fresh air.

He didn't say that it couldn't be measured accurately because the instruments weren't precise enough.

Instead, he repeatedly emphasized: "Please remember, uncertainty is definitely not a flaw in human technological development."

"It's not because our hands are shaking, not because the microscope isn't advanced enough, and even less because the electron is too small so our mortal eyes cannot see it clearly. Even if you possess God's instrument, you still cannot measure it accurately."

"Because this is determined by the mathematical structure of the quantum state itself. This is the Fourier transform property of the wave function! When the distribution in position space narrows, the distribution in momentum space inevitably widens. This is the geometric rule in Hilbert space, the ironclad law at the bottom of the universe."

Jiang Lin watched this part relatively quickly.

Because for these hardcore mathematical derivations, he had suffered hardships and shed sweat over them, crushing them and swallowing them into his stomach.

In order to popularize science to the general public, Professor Lu Zhixing omitted some extremely complicated mathematical derivation details in the video, such as the proof of the non-commutativity of operators in functional analysis.

Jiang Lin could keenly sense where those omitted steps were.

But he didn't feel that Professor Lu Zhixing was perfunctorily brushing it off.

He deeply understood that science popularization was not compiling textbooks.

Facing ordinary viewers, some overly steep mathematical bridges had to be built a bit narrower and gentler first, otherwise viewers would plunge into the abyss at the very first step.

In the second video, the difficulty suddenly increased, talking about the most profound verdict in the history of Physics: Bell's Inequality.

At the very beginning of the video, Professor Lu Zhixing put away his previous ease, his expression solemn: "Friendly reminder, the logical density of this video is extremely large, and you might need to pause many times."

Jiang Lin indeed paused many times.

It wasn't because it involved some complex calculus that he couldn't understand.

But because he didn't dare let himself muddle through with a vague state of "I seem to understand it."

Locality, reality, hidden variables...

Every single word he had seen before.

Yet when Professor Lu Zhixing reconnected them with a rigorous logical chain, it still required Jiang Lin to stop and re-examine the physical images and philosophical premises behind these concepts in his mind.

When seeing Professor Lu Zhixing talk about seeing the Aspect experiment, which confirmed that entangled photon pairs violated Bell's Inequality and yielded a result of 2 square root of 2, Jiang Lin dragged the progress bar back once.

Professor Lu Zhixing only talked about the basic logic and results of the experiment, proving the bankruptcy of local realism, but he didn't elaborate on the loophole issues existing in the early stages of the experiment.

However, this was also very normal.

The video was already twenty minutes long.

If short videos were to delve deeper into what locality loopholes and detection efficiency loopholes are, the brains of the vast majority of viewers would crash, and they would immediately swipe away.

But Jiang Lin's pen stopped right there.

He wrote on the draft paper: [Aspect's Experiment: It ruled out hidden variables, but what kind of category did it actually rule out? Were they all hidden variables, or just the hidden variables that rely on the premise of locality?]

Below that, he added: [Regarding experimental loopholes (loophole-free experiments): How is the detection efficiency loophole closed? In the locality loophole, is the random selection of the measurement polarization direction absolutely independent?]

He didn't look it up immediately.

He just left the questions there for now.

The fourth series, which was also the account's final series, was called: [Quantum Mechanics and Our Intuition]

This series currently only had two videos.

The first one talked about human neural synapses and intuition, and why they were only suited for processing the macroscopic, intermediate-scale world—because this was beneficial for ancient humans to evade lions on the African savanna.

Evolution didn't require us to understand Quantum Mechanics.

Coming to the second video, it discussed that famous debate of the century, the argument between Bohr and Einstein over whether God actually rolled dice.

Professor Lu Zhixing spent several minutes describing Einstein's stance with extreme objectivity.

He didn't portray the elderly Einstein as a stubborn and obstinate old die-hard, like some second-rate popular science works did.

"Everyone must understand one thing: Einstein didn't oppose the Copenhagen interpretation because he didn't understand or couldn't calculate the Schrödinger equation."

"On the contrary, Einstein was one of the very few people in all of humanity who understood Quantum Mechanics best; the photoelectric effect was proposed by him."

"It's just that being able to understand its mathematical structure doesn't mean accepting it philosophically. The absolute causality and objective reality that Quantum Mechanics demands physicists to abandon were not minor assumptions that Einstein could casually throw away; they were the foundational cornerstone with which he built the entire edifice of the physical world, his ultimate conviction of what the universe ought to be. He could not tolerate a universe where the moon didn't exist just because no one was looking at it."

Seeing this, Jiang Lin closed the video and leaned back against his chair.

He had no qualifications to say he understood Einstein.

However, he understood the massive chasm between being unable to understand and being unable to accept, as described in the video, better than anyone else.

It took him twelve years and every means possible to barely deduce the foundational parts of Quantum Mechanics to around seventy percent proficiency.

During this process, the most frequent mistakes he made were by no means getting the signs wrong in calculus or reversing matrix multiplication.

The mistakes he made most often were those erroneous intuitions lurking deep within his cognition.

Like ghosts, they always dragged him back into the macroscopic quagmire just when he was about to touch the microscopic truth.

He had to force himself to accept many things that defied common sense.

Yet accepting did not equal being comfortable.

Most of the time, acceptance was simply because the flashlight in your hand only illuminated this one rugged path, while all around was a bottomless abyss.

You had no other road to walk.

Twenty-three videos.

He watched for nearly five hours, not putting down his phone even while eating dinner.

This caused Zhang Xiufen to nag for quite a while at the dinner table, feeling distressed that her son might have caught a cold going out today or become obsessed due to too much study pressure.

Jiang Jianguo chimed in from the side to smooth things over, saying the child must be watching some famous teacher's online classes.

Half past eight in the evening.

Until the screen of his dad's old phone popped up a red warning box stating battery level was below 1%, Jiang Lin finally let out a long, stale breath, rubbed his slightly sore eyes, plugged the phone into the charging cable, and placed it flat on the corner of the table.

His brain was currently in a state of excitement and clarity after high-speed operation, so he took out paper and a pen and began listing questions on it.

Three questions.

The first one, regarding Bell's Inequality.

[Teacher Lu, regarding the experimental tests of Bell's Inequality. You mentioned in the video that it ruled out hidden variables. But my confusion lies in: did it rule out all possible hidden variable theories, or more accurately, did it merely rule out that specific class of hidden variable models satisfying the assumptions of locality and reality? What did the Aspect's Experiment specifically strip away mathematically? In addition, how did subsequent loophole-free experiments mainly plug the detection efficiency loophole and the locality loophole?]

After finishing the first paragraph, Jiang Lin reviewed his choice of words.

He moved the tip of his pen to the next line.

The second one, regarding the double-slit experiment.

[You said that when there is no measurement, whether which slit is taken has meaning. I would like to ask in depth: is this lack of meaning merely a self-prescription within the current theoretical framework of Copenhagen Quantum Mechanics (i.e., the theory does not discuss unobservable things), or does it point more forcefully to the objective properties of nature—that nature itself does not allow us to pose such classical questions? If a more complete theory containing hidden variables (such as Bohmian mechanics) emerges in the future, is it possible for this question to regain physical significance?]

After writing these two questions, Jiang Lin's wrist relaxed slightly.

This was pure theoretical discussion.

Next was the core question that exposed the weaknesses of his own mathematical foundation.

The third one, regarding Heisenberg's uncertainty principle and state preparation.

[Regarding the uncertainty relation, my understanding is that what it restricts is the joint compression of the distribution widths of certain conjugate physical quantities in the same quantum state. Therefore, what different preparation methods (such as changing filtering devices) change is the structure of the state itself, rather than bypassing the measurement disturbance of uncertainty on the existing state. Is this direction of understanding accurate? Will my residual classical image of joint compression affect the subsequent understanding of measurement theory?]

After writing the third question, Jiang Lin read through the whole thing from start to finish.

After a brief thought, he felt that this straightforward tone might make the other person feel like he was coming to pick a fight or argue for the sake of arguing.

Therefore, next to the third question, he added a sentence.

[My foundation is limited, and this question might not be expressed accurately enough, even appearing somewhat layman. If there is a fundamental logical bias in my direction of understanding, I kindly ask Teacher Lu to point it out directly. I would be extremely grateful.]

The questions were written and finalized.

Jiang Lin picked up the phone, which had already charged quite a bit, and unplugged the charging cable.

He opened the Douyin homepage of Quantum Mechanics Isn't That Mystical and clicked the direct message button.

The interface jumped to a blank dialogue box.

Jiang Lin began typing character by character on the nine-key keyboard.

Hello, Teacher Lu.

I have finished watching the several series of videos on your account regarding the double-slit experiment, the observer effect, the uncertainty principle, and Bell's inequality. I have watched some parts repeatedly, felt deeply inspired, and have three questions I would like to consult you about.

Let me first brief you on my situation, so as not to leave you wondering where to begin answering. I have self-studied General Physics, Linear Algebra, and a portion of the basics of Quantum Mechanics.

Currently, I can achieve an accuracy rate of around seventy percent on basic calculation questions in Quantum Mechanics, but the angular momentum part is currently progressing with difficulty, especially since the mathematical derivation foundation regarding spherical harmonics is not yet stable.

Regarding the following three questions, I am not looking for a popular science conclusion aimed at the general public, but rather trying to confirm where exactly the gap in thinking lies within the understanding system I constructed while groping in the dark on my own.

...

Even with the draft as a base, Jiang Lin still sat in his chair, deleting and modifying, spending nearly a whole hour typing out the private message of just over a thousand characters.

It was not because typing on the phone was slow, nor because the questions were difficult to write.

Rather, it was because he had to meticulously control every single vocabulary word like a mine-sweeper walking through a minefield.

He had to let Professor Lu Zhixing on the other side of the network know crystal clearly which step he, the questioner, had already thought to, and which specific coordinate point he was stuck at.

Which dime-a-dozen answers he had already seen and didn't need to be told again, and which subtle turning points he still dared not claim to understand.

After finishing writing, he silently read through it from start to finish in his mind.

He deleted two sentences explaining his self-study experience that seemed somewhat verbose.

He precisely changed the philosophically ambiguous phrasing in the second question—such as whether it indicated that nature is not real—into whether it indicated that a class of realism models satisfying assumptions such as locality does not hold.

He replaced all the subjectively colored "I feel" with the objectively rigorous "my understanding is".

He changed the demand-implying "seeking an answer" to the lowered-stance "wanting to ask you to correct me".

Finally, everything was confirmed to be correct, and the private message was sent out.

The message box quieted down.

There was no automated reply of any kind.

Jiang Lin exited the private message interface.

In the lower right corner of his retina, on the system countdown that only he could see.

The numbers were ticking away second by second.

[29:05:31:44]

29 days, 3 hours, 31 minutes, and 44 seconds.

There was still some time before the next forced descent into the Wasteland World.

Jiang Lin stood up, stretched, returned the phone to the living room, and placed it beside his father, who was still watching an anti-Japanese drama.