Chapter 158: The Correspondence Principle

By all rights, the mornings at the Tower of Truth were usually accompanied by the elegant chime of bells and the low hum of mages chanting incantations.

But today, that elegance was utterly torn apart by an emotion called hysteria.

The floor of the “Journal of Truth” editorial office was covered in letters, like a fresh fall of snow.

The shouting nearly blew the roof off.

“Cancel my subscription! I want to cancel!”

An old mage in a red robe had rolled the newly issued journal into a club and was frantically beating it against the reception desk.

He was a senior professor of the Elemental School, and his usually dignified face was now the color of pig’s liver.

“Absurd! Utterly absurd! Have the Eisenbergs gone mad? The atom is empty? Electrons are jumping down stairs? Then how does my fireball form? Through faith?”

The receptionist, a young, low-circle mage, cowered behind the counter, trembling, still clutching a stack of supplements that hadn’t yet been sent out.

“Professor, it has been reviewed…”

“Reviewed? Who reviewed it?”

The old mage threw the journal on the floor, pointing at the target-like diagram of the atomic model on the cover.

“If an electron’s movement is not continuous, then where does it go in the time between jumping from one orbit to another? Does it teleport? Or was it eaten by the Creator God?”

A dead silence fell over the hall.

No one could answer that question.

Teleportation.

This word, which had previously only existed in high-circle spatial magic, was now attached to the tiniest of particles.

If electrons could teleport, then the foundational blocks that built this world weren’t solid bricks, but a bunch of flickering, jumping ghosts.

***

The highest conference room of the Tower of Truth.

Archmage Samuel sat at the wide conference table. He wore a simple gray mage robe, his face was gaunt, but his eyes were extremely sharp.

He held a cup of black tea, its surface rippling.

He stared at those ripples for a long time.

‘Is it continuous?’ he mused.

Before, he would have said without hesitation that water waves, of course, spread continuously.

But now, looking at those ripples, his mind uncontrollably conjured the paper’s description of electrons only being able to transition between fixed energy levels, like jumping on invisible steps.

If those tiny particles could really only advance one unit at a time, was the world he knew also filled with such jumps?

“Dammit.”

Samuel cursed and put the teacup down heavily.

On the sofa opposite him, Klein was peeling an orange.

The peel came off in one complete piece, without even a bit of pulp attached.

“It’s about to turn into a brawl outside.”

Samuel rubbed his temples. “The elemental faction feels that this paper is digging up their ancestral graves.”

“That’s their problem.” Klein broke off a segment of the orange and put it in his mouth.

“You’re certainly calm.”

Samuel glared at him. “Where’s Lia?”

“Sleeping.”

“Sleeping? She can sleep at a time like this?”

“She was tired last night.”

Klein’s tone was flat, without any fluctuation.

Samuel nearly choked and coughed for a long time.

He eyed Klein suspiciously, trying to read something from that poker face, but failed.

Klein’s face was thicker than the city walls.

“Let’s be serious.”

Klein wiped his hands. “This paper cannot be questioned. Horace’s data is too solid. The derivation of the Balmer formula is right there. If anyone can derive it using classical electromagnetic theory, I’ll eat this tower.”

Samuel sighed, his body sinking into the chair, aging several years in an instant.

“I know it can’t be questioned. It’s… too perfect. So perfect it’s despairing.”

As an Eighth Circle Archmage, Samuel could of course understand those few lines of equations.

It was precisely because he understood that he found it terrifying.

Before, everyone was playing ostrich.

When Lia proposed the energy quantum, everyone could still say it was just a special case for black-body radiation, just a calculation trick.

As long as one didn’t pull their head out of the sand, the world was still a continuous God.

But now, the Eisenbergs had kicked the sand everywhere.

They had taken that damned h, the constant that represented the world being made of discrete portions, and stuffed it directly into the belly of the atom.

The spectrum was no longer a puzzle, but evidence.

Each spectral line was the footprint of an electron playing hopscotch in the microscopic world.

“Admit it.”

Klein stood up, straightening a non-existent wrinkle on his cuff.

“The time for being an ostrich is over.”

***

In the afternoon, in the third lecture hall of the National Magic Academy.

This was usually where “Intermediate Magical Dynamics” was taught. But today, the professor on the stage couldn’t continue his lecture.

Maxwell’s equations were written on the blackboard.

Below sat over a hundred apprentices, each with a copy of that hastily printed “Journal of Truth” open on their desk.

“Professor.”

A male apprentice with thick glasses raised his hand, his other hand pressing on the journal.

“According to the derivation here, if an electron orbits the nucleus without radiating energy, it means that at this scale, Maxwell’s equations are invalid. Then why do we still have to learn this?”

The hand holding the chalk froze in mid-air.

“This is foundational!”

The professor asserted with authority. “The macroscopic world still follows these laws! Does the trajectory of your fireball also jump from place to place?”

Another female student stood up, her voice sharp. “If we are made of atoms, and atoms are made of electrons, and electrons jump… then why aren’t we also jumping?”

A burst of laughter erupted in the classroom.

But there was a sense of panic in the laughter.

Because no one knew the answer.

Just then, the back door of the classroom was pushed open.

Lia walked in, while Adèle was daydreaming outside.

She was wearing the gray everyday clothes Klein had bought, her hair casually tied in a knot, and she held a cup of steaming coffee in her hand.

She looked well-rested.

The laughter in the classroom died down instantly. All eyes were on her.

The female student looked at Lia nervously. “Lia… stop…”

Lia walked up to the female student, took the journal from her desk, and flipped to that page.

“Who says you aren’t jumping?”

Lia took a sip of coffee. Her voice wasn’t loud, but it was clearly audible in the quiet classroom.

“It’s just that the steps you take are too small.”

She turned and picked up a piece of chalk from the lectern.

The professor subconsciously took a step back, giving her the blackboard.

Lia drew a dense wavy line on the blackboard.

“Planck’s constant is very small. So small it has dozens of zeros after the decimal point.”

“For something as light as a speck of dust, like an electron, this step is very high, so it must jump.”

Lia drew a huge sphere next to the wavy line.

“But for you, for macroscopic objects, the mass is too great.”

“A single step is compressed until it’s infinitely flat, so flat that it looks like a smooth slope.”

Lia tossed the chalk back into the box and dusted off her hands.

“You are still playing hopscotch. It’s just that your squares are too dense, so dense that you can’t even feel it yourself.”

“This is why Maxwell is still a god in the macroscopic world, but in the microscopic world, he has to make way.”

The classroom was silent.

The male student who had asked the question gaped, his glasses sliding down to the tip of his nose.

“The correspondence principle…”

In the corner, an upperclassman who had been silent all along muttered to himself.

“The two theories coincide at the limit…”

Lia glanced at that apprentice and nodded in approval.

“That’s right. The new theory isn’t meant to kill the old one, but to encompass it.”

She picked up her coffee and scanned the classroom.

“Don’t throw away your textbooks. Unless you plan to become an electron in the microscopic world in the future, you still have to take this exam.”

With that, she turned and walked out of the classroom.

Only after her figure disappeared down the corridor did a thunderous discussion erupt in the room.

The professor wiped the cold sweat from his forehead, looked at the simple diagram on the blackboard, and gave a bitter smile.

He knew that the content of this class would have to be rewritten in the future.

***

In the corridor.

Adèle followed behind Lia, her face full of admiration.

“That was so cool! Lia, when you said ‘Don’t throw away your textbooks,’ it was just epic!”

Adèle was so excited she was practically dancing. “Did you see the professor who kept asking questions? His face turned green!”

“I was just telling the truth,” Lia yawned.

“But…”

Adèle leaned closer, lowering her voice.

“Now everyone is calling you the spokesperson for the ‘Quantum Demon.’ Some are even saying that Mrs. Eisenberg’s paper was actually instigated by you, with the aim of destroying classical physics to establish your own academic empire.”

Lia almost spat out her coffee.

“Academic empire? I can’t even be bothered to grade homework.”

“But this really has changed everything.”

Adèle caressed the yew wood staff in her hand.

“News came from the Alchemy Association. Master Griffin—that old man—announced today that he has found the laws of elemental combination.”

“Oh?”

Lia’s interest was piqued.

“He said that if electrons are arranged in layers of orbits, then the number of electrons in the outermost layer determines who that element wants to bond with.”

Adèle tried hard to recall the announcement she had seen. “For example, some elements are missing one electron in their outermost layer, while some have one extra. When they come together, it’s a perfect match.”

Lia smiled.

“The octet rule.”

“The prototype of valence bond theory.”

‘There are far more smart people in this world than she had imagined. Just give them a key, and they can kick the door down themselves.’

“It seems alchemy won’t have to rely on luck and metaphysics anymore,” Lia said.

“Yeah.”

Adèle sighed. “Before, alchemy was all about ‘feeling.’ Now, it’s all about math. I heard several old alchemists got so angry from not being able to calculate the number of electrons that they smashed their crucibles.”

As the two were talking, a tall, slender figure appeared ahead.

Klein was leaning against a window, holding a document.

The sunlight fell on him, coating him in a golden edge.

When Lia approached, he stood up straight.

“I saw you went into a classroom. Was there a problem with the teacher’s lecture?”

“It’s fine, just a matter of changing perspective.”

Lia shrugged. “Give them some time. Once they get used to this concept, they’ll find it’s actually pretty cool.”

Klein handed the document in his hand to Lia. “This just arrived from the Alchemy Association. Griffin has requested a meeting with you to discuss the issue of ‘electron sharing.’

He thinks that since electrons have wave-like properties, when they are shared, they might form some kind of… cloud?”

Lia took the document, her eyebrows raising.

“An electron cloud?”

“That’s a bit of a leap.”

“Not necessarily.”

Lia closed the document. “Let him struggle with it himself for now. I haven’t even figured it out myself yet. I’ll think about these things when I have the time.”

The corner of Klein’s mouth lifted imperceptibly.

He naturally took Lia’s hand.

“Let’s go.”

“Mmm.”

Lia instantly perked up, grabbing Klein’s sleeve and dragging him upstairs.

Adèle stood where she was, watching their departing backs.

She suddenly felt that the so-called “quantized world” wasn’t so cold after all.

At least, some things were continuous.

Like the look in the mentor’s eyes when he looked at Lia, and the natural force with which Lia pulled on his sleeve.

“Everything.”

Adèle chewed a lemon drop sourly. “Even public displays of affection are served in discrete portions, and they’re force-fed.”

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