41: Chapter 41 The Elephant-Feeling Man in the Dark Room

Three days later.

The lively atmosphere of the New Year festival gradually subsided, leaving only the occasional loud snap-firecracker set off by some mischievous child hiding in a corner, startlingly loud.

Emerging from the endless barrage of greetings from visiting relatives—exchanging pleasantries, asking what job Professor Lu Zhixing now has, how much he makes a month, and whether science communication can put food on the table—he finally had time to sit in front of his dual-screen computer and handle some truly personal matters of his own.

He casually pulled a can of sugar-free oolong tea from the side.

The icy liquid slid down his throat, and the lingering social exhaustion in his brain, typical of a carbon-based lifeform, was finally largely dispelled.

After dealing with a backlog of emails and some trivial utility bills, he dragged his mouse, opened the Douyin creator backend, and checked his direct message list.

He hadn't updated during the Spring Festival holiday, and the backend data was running tepidly.

From New Year's Eve before the holiday until now, there were only six long direct messages worth singling out to read.

Professor Lu Zhixing narrowed his eyes and went through them one by one.

The first one had an anime two-dimensional avatar and asked quite righteously: "Teacher Lu, let me just ask you one thing, is light ultimately a particle or a wave? Give me a straight answer."

Professor Lu Zhixing's mouth twitched.

This was practically a daily classic in the science communication world; if he didn't answer it a few times a day, it felt like he hadn't gone to work.

The general public always habitually used the dualistic opposition of the macroscopic world to mechanically apply quantum scale things, black and white, either-or.

Just like asking whether a platypus is a duck or a beast, the question itself carried a sense of crude pulling and tearing.

However, he still tapped on the keyboard and replied: "This question cannot be answered with a multiple-choice of two; just like when you ask whether a cylinder is a rectangle or a circle, it depends on which dimension you look at it from. It is recommended to watch the first episode of the double-slit experiment pinned on my homepage first, and watch it patiently."

By the way, he attached the video link.

The avatar of the second one was a Shiba Inu wearing a mask of pain, and judging by the tone, it was estimated to be a junior undergraduate: "Master, save me! Quantum Mechanics is going to start next semester. Is this course difficult, and will I fail if I choose it? I just barely flew low over Theoretical Mechanics, and Electrodynamics is half-dead. With Quantum Mechanics coming up next semester, am I beyond saving? QAQ."

Seeing this cyber wailing struggling on the edge of the passing line, the image of a college student scratching their ears and cheeks in the study room instantly popped into Professor Lu Zhixing's mind.

Although not even a face was shown, this clear stupidity and pure anxiety were quite recognizable.

He couldn't help smiling, his fingers moving swiftly across the keyboard: "Difficult, definitely difficult. Whether you fail depends on whether you are willing to set aside your deeply rooted classical Physics intuition first and rebuild your worldview from scratch. Play a few fewer games, calculate a few more problems, good luck."

The third one was a seemingly serious scenery avatar, coming straight up to ask for textbook recommendations.

Professor Lu Zhixing wasn't stingy and gave two.

One was Griffith's Introduction to Quantum Mechanics, with a brief note written: "Suitable for beginners, relatively low mathematical threshold, intuitive imagery. The other is Zeng Jinyan's Volume 1, with an added note: suitable for those who want to find abuse or need to systematically grind problems to cope with exams, the derivation is very detailed, but a bit dry."

The fourth and fifth ones, the questions were simply too broad.

One asked whether Quantum Mechanics can explain out-of-body experiences, and the other asked if the ultimate meaning of the universe is quantum entanglement.

For this kind of question treating Physics as a substitute for metaphysics, Professor Lu Zhixing was already used to it.

Having done science communication for a long time, what he felt most often was not the public's desire for science, but the public's obsession with trying to wrap their superstition in scientific vocabulary.

However, he didn't mock them either, just calmly replied to each with a few harmless pleasantries, such as that there is currently no empirical evidence in the scientific community for such phenomena and so on, and then casually swiped past.

Only the last one was left.

For this sixth one, when he clicked on it, Professor Lu Zhixing was holding that can of oolong tea, his posture relaxed to the point of being a bit casual.

He originally just planned to scan the beginning like sweeping mines, quickly glance at it to judge whether it was a novice asking a question, fans urging for updates, or a troll coming to pick a fight.

Just by glancing at the two sentences of background explanation at the beginning, his hand holding the beverage can paused mid-air, then he put down the tea can, and his back, which had been leaning back slightly, instantly straightened.

Then, he scrolled the wheel, pulled the progress bar back to the very top, and started reading from the beginning.

Teacher Lu, hello.

I finished watching several videos in your account regarding the double-slit experiment, the observer effect, the uncertainty principle, and Bell's inequality, and I have a few questions to ask for advice.

...

The density of questions in this direct message was completely on a different scale from the previous five.

The previous ones were splashes; this one was trying to deep-dive.

He looked down.

Seeing that basic questions were seventy percent mastered, angular momentum was being learned, and spherical harmonics were still unstable, his brows twitched.

This description didn't sound like the tone of an ordinary science communication enthusiast.

After watching the double-slit experiment, an ordinary enthusiast's first reaction would definitely be some mystical emotion like "So the moon only exists when I look at it"; who would have nothing better to do than mention spherical harmonics?

But it didn't sound like the tone of Physics undergraduates asking about homework either.

If it were a Physics student with relatively complete training, when mentioning angular momentum and spherical harmonics, they would usually expose a whole set of classroom traces along the way.

But this direct message didn't have that familiar classroom accent; instead, it felt like someone had stubbornly gnawed their way through textbooks and videos all the way here, yet still hadn't completely grasped the tools firmly.

Trained students might get stuck on perturbation theory or scattering theory, but they would never use a guilty word like "unstable" to describe their mastery of mathematical tools.

Looking further down, three questions unfolded one by one.

After reading it the first time, he didn't immediately put his hands back on the keyboard to type those ready-made clichés.

This was not only a disrespect to the sender, but also a desecration of his own professionalism.

He stood up, walked over to the bookshelf, his gaze swept across rows of bulky Physics monographs, and then retreated back to the desk.

Sitting back in front of the computer, he picked up a habitual black neutral pen from the desktop, grabbed a light-yellow sticky note, and wrote down three words.

Bell experiments, interpretation boundaries, preparation and uncertainty.

After writing these three words, he spun the pen barrel between his fingers and began reading the direct message a second time.

This time, he read extremely slowly, as if chewing on the thinking trajectory behind the words.

This very first question was asked very accurately.

"You said that Bell's inequality ruled out hidden variables; I have been uncertain here. Did it only rule out 'local hidden variables'? In other words, it's not that all hidden variables are dead, but rather those models that both want particles to carry answers in advance and do not allow distant measurement choices to affect the results here—those are the ones that died, right? Would my understanding be too crude?"

Professor Lu Zhixing stared at this sentence for quite a while, and couldn't help cursing inwardly: He finally waited for an audience who actually knew their stuff.

The other party didn't badger like most amateur scientists, asking whether Bell's inequality proved that the world is a virtual matrix program.

Nor did they act like sci-fi fans, excitedly asking whether quantum entanglement could be used to build superluminal communicators.

They simply struck right at the core jugular artery of this theory with a single knife.

The premise of the assumption.

This difference was too important, so important that many university teachers would muddle through it vaguely when giving lectures.

The Aspect experiment did not crudely pronounce Einstein completely wrong.

What it truly closed was the path of local hidden variable theory. If you want to retain the deterministic results that already existed before every measurement, and also want to retain a strictly local causal image, then the experimental data will go against you.

You can choose to abandon a certain realism, or you can choose to accept non-local structures, and you can even question measurement independence, but you can no longer naively cram the classical particle image intact back into the quantum world.

The other party keenly grasped the fish and the bear's paw of locality and realism that could not both be had.

The second question made Professor Lu Zhixing feel a long-lost excitement, an excitement that made him reach into his pocket to find a cigarette, only to realize after touching empty air that he had quit smoking for half a year.

"When there is no measurement, does it matter which slit is taken?"

He had indeed said this sentence in the video, used as the ending of a suspense hook.

But he didn't dare to elaborate on it in the video.

Because as a science communication blogger, he knew too well what kind of bloody consequences would be triggered once he expanded on this question.

Once expanded, it would inevitably slide into the interpretation quagmire of Quantum Mechanics.

To put it crudely, many textbook-style answers would compress it into four words: Shut up and calculate.

The many-worlds interpretation would not answer the question as to which slit the particle actually took, but rather say that the wave function of the entire system always evolves unitarily, and the particles, instruments, and environment become entangled, and then through decoherence form branches that hardly interfere with each other anymore.

The so-called splitting of worlds was just a popular way of describing this branching structure.

While Bohmian mechanics would tell you that particles have definite trajectories, it's just that you don't know how that mysterious quantum potential guides them.

If he went any further, ordinary viewers would either doze off or start fighting tooth and nail in the comment section over their respective belief systems.

But in this direct message, there was no hostility wishing to pick a fight, nor any arrogance with a presupposed stance.

The other party was simply inquiring about boundaries in an extremely pure manner.

Asking whether, when mathematical equations reached their end and physicists began using language to depict that imagery, it was ultimately the truth or mere guesswork?

The third question was the most interesting part of this entire direct message, and the one that most exposed the questioner's hand.

When discussing Heisenberg's Uncertainty Principle, the other party's general direction was entirely correct.

He understood that this was not measurement interference caused by instrument precision, but an inherent property of things.

But when describing state preparation, the other party used a term.

"Joint compression restricting distribution width."

It was precisely these ten short characters that made Professor Lu Zhixing certain of his judgment.

This wasn't a mistake; it was merely a deviation of about 0.1 millimeters on the track leading to the truth.

It was like someone covered in mud, locked in a pitch-black room where they couldn't even see their own hand.

Inside the room was a behemoth named Quantum Mechanics.

With no guidance, no textbooks, and no flashlight, this person could only rely on an extremely keen sense of touch to grope around bit by bit, yet managed to forcefully piece together an outline of this elephant that was remarkably close to reality.

But at some extremely minute corner, such as the direction of the wrinkles on the elephant's ears, a tiny gap arose between him and those orthodox students outside the door who held standard blueprints and turned on searchlights.

The other party believed that position and momentum were two independently existing objective distributions, merely forcibly packaged and compressed together by some external cosmic law, waxing and waning against each other.

This deviation could not be reflected at all when doing basic calculation problems.

You could even use it to cope with final exams and still get a high score.

But once one continued to dig deeper, walking into the deep waters of quantum measurement theory, the commutation relations of operators, and the inner product structure of Hilbert space, this lingering classical particle intuition would turn into a massive stumbling block, looping back to trip one up until blood was shed.

Professor Lu Zhixing sighed.

This direct message was tightly structured, with its logic interlocking closely.

The person asking clearly knew what they wanted to ask, knew at which coordinate their current thinking had stopped, and more importantly, knew where they dared not claim understanding.

This was a rare and precious humility belonging to a seeker of knowledge.

Professor Lu Zhixing moved his mouse, dragging this direct message out of the default list and into a separate folder he had created privately.

The name of the folder was very simple: "Serious Questions".

This folder had been created for over a year, and originally contained only four lonely direct messages.

Now it had become five.

He opened a blank Word document, pulled his keyboard closer, and began drafting a reply.

Discussions of this level were too hasty to type directly into the dialogue box; they had to be carefully weighed.

Part one, answering the Bell inequality.

He wrote down the basic logic of the Aspect experiment, analyzed the mathematical structure of local hidden variable theories, and explained to the other party that what the experiment tested was never a single variable, but a set of hypothetical models jointly constituted by locality and reality.

He even casually expanded on it, writing that the later so-called loophole-free experiments were mainly designed to handle detection efficiency loopholes and locality loopholes, as well as issues related to random choices in experiments.

This section was over three hundred words long, without long-winded arguments or piling up intimidating formulas, but the subject, verb, and object of every sentence had been rigorously scrutinized to ensure conceptual accuracy as much as possible.

Part two was what he wrote the slowest, stopping several times to deliberate.

Regarding whether it was meaningful to ask which slit was taken when there was no measurement.

At first, he typed: "This question does not have a clean answer that all physicists agree on."

Staring at the screen for three seconds, he pressed the backspace key and deleted the sentence completely.

Re-typing: "This question does not have a clean answer jointly accepted by current different quantum interpretations."

After drawing the boundaries clearly, he patiently explained that under the orthodox view of the Copenhagen school, probing the trajectory when unobserved was usually regarded as an inappropriate metaphysical question, and Physics only cared about the statistical regularities of observation results.

Then, changing the subject, he explained that in the Many-Worlds interpretation, this question would be rewritten as wave function branching and decoherence effects brought about by the environment.

In Bohmian mechanics, particles indeed had definite trajectories, but this cost was not small; the evolution of the system had to be guided by the wave function, and the wave function of a multi-particle system usually lived in configuration space, with the guiding relation having a non-local dependence on the state of distant systems.

It was not controllable superluminal communication, yet it indeed sacrificed the local causal intuition in the classical sense.

Writing to this point, Professor Lu Zhixing felt his mouth dry, picked up the Oolong tea beside him and took a large gulp, the icy feeling keeping his brain clear.

Then he continued typing on the keyboard: "You must understand that experiments rule out certain dead ends that don't work, but nature hasn't chosen a specific interpretation for you. Knowing the difference between the hard results of mathematical calculations and the soft stories of philosophical interpretations is far more important than rote memorization of a standard answer."

As for the third part, which was pointing out that subtle crack of the other party.

Professor Lu Zhixing appeared exceptionally cautious; he did not want to discourage this soul groping in the dark.

He wrote: "You said that different preparation methods change the state itself rather than simply bypassing the uncertainty interference; this direction is basically correct, and your intuition is exceptionally brilliant."

"However, you later used the phrase 'joint compression restricting distribution width'."

"I must remind you to be careful not to understand it as two objective distributions that already independently exist, being forcibly pinched together by some external rule."

"To be more precise, the distribution of physical quantities comes from the same quantum state, displaying statistical structures under different representations or different operators."

"To be more specific, the wave function in the position representation and the wave function in the momentum representation are not two mutually independent lists, but the expansion of the same quantum state in different representations."

"The two are connected by a Fourier transform."

"And the more general uncertainty relation comes from non-commuting operators and the Cauchy-Schwarz inequality."

"It is not that external rules forcibly bind the two distributions together, but that the structure of the quantum state itself does not allow you to compress both types of expansions arbitrarily narrow at the same time."

After typing this passage, he thought about it, and fearing that the other party might not fully understand, he added a plain-spoken paragraph.

"Your direction of understanding on this problem is basically accurate, but your phrasing implies that there is still a trace of classical particle imagery left in your brain. This residue doesn't affect your basic problems for now, and can even help you quickly build intuition. But take my advice: when you go deeper and learn measurement theory, this intuition will circle back to cause you massive trouble. Try to embrace pure superposition of states."

After finishing everything, Professor Lu Zhixing silently read through this nearly thousand-word reply from start to finish.

Confirming that he wasn't putting on airs or showing off his book-learning, nor rudely brushing off the problem with obscure terminology, everything was struck at a scale that could just hold the weight of the other party's thoughts.

Just before copying it into the dialogue box, driven by a strong curiosity, he added a final line at the end.

"Let me ask one more question, where did you learn these? If it's self-taught, have you systematically studied Mathematical Physics Methods and Linear Algebra?"

Because the word count was too long, he split it into two messages, copied, pasted, and clicked send.

The green chat bubbles popped out.

Professor Lu Zhixing felt as if he had completed a high-intensity mental marathon, stretching long and lazily as his joints made cracking sounds.

Picking up the bottomed can of Oolong tea, he pushed away the gaming chair and strolled slowly to the floor-to-ceiling window of the study.

The residential area downstairs had completely quieted down by now, the yellowish halo of the street lamps appearing somewhat thin in the cold wind.

On the distant edge of the city, scattered fireworks unwilling to be lonely darted into the night sky, lighting up briefly in the ink-blue canopy, blooming with a faint light, and then quickly extinguishing to return to silence.

It was just like unobserved quantum fluctuations time and again.

A strong curiosity suddenly welled up in his heart.

At the other end of that network cable, who on earth was that person without standard blueprints, groping around for the giant elephant alone in the dark room?

In that unknown corner, who was gazing up at the starry sky with such earnestness amidst the embers of the holiday?