Chapter 160: Fine Structure

If you were to stand at the top of the Tower of Truth and look down today, you would find that the elemental mages, who usually walk with their noses in the air, were now like a swarm of worker bees that had lost their queen, buzzing anxiously in the square.

They waved parchments in their hands, muttering strange words like “valence electrons” and “covalent bonds.”

Lia sat in a wicker chair on the second-floor terrace of her own tower, holding a cup of black tea with a double dose of sugar, contentedly watching the farce below.

“They look like they’re about to go mad,” Adèle said, leaning on the railing with a sympathetic expression.

“Just now, I saw Master Griffin—the president of the Alchemy Association—he was running and crying at the same time, still clutching a copy of the ‘Journal of Truth’.”

“Those are tears of joy.”

Lia blew on the steam from her tea. “Or perhaps it’s the unbearable realization that the alchemical experiments of the first eighty years of his life were just a case of a blind cat stumbling upon a dead mouse.”

Just yesterday afternoon, Lia’s paper on “The Shell Structure of the Atom and the Essence of the Chemical Bond” was officially published.

It was not just a paper; it was a verdict.

It pronounced the death sentence on the era of classical alchemy, which relied on “gut feelings,” “metaphysics,” and “judging by the fire.”

In its place were the irrefutable laws of electron configuration.

“Lia.”

Familiar, hurried footsteps came from behind. Klein pushed open the glass door to the terrace, holding an express document that had just arrived.

His face was even paler than usual today, with faint dark circles under his eyes, a clear sign of another all-nighter.

“It seems you didn’t sleep well,” Lia said, putting down her teacup, a knowing question in her voice.

“Couldn’t sleep.”

Klein walked over to her and handed her the document. “Sleep spells don’t work, and it’s impossible to sleep anyway. You’ve started a fire, and now the entire magical world is burning. Look at this.”

Lia took the document. It was an experimental report from a distant northern province, signed by a mage named Henry.

“Henry?”

Adèle raised an eyebrow. “I’ve heard of him. Isn’t he that weirdo who likes to bombard all sorts of metal plates with electron streams all day?”

“That’s him.”

Klein’s voice rang out.

“After seeing your and Horace’s papers, he adjusted his experiment. He bombarded dozens of elements, from lead to gold, with high-energy electron streams, and then measured the frequency of the emitted X-rays.”

Lia unfolded the report.

There was only one chart on it. The horizontal axis was the element’s atomic number on the periodic table, and the vertical axis was the square root of the X-ray frequency.

The points were arranged in a perfectly straight line.

Without any deviation, the line was as straight as if it had been drawn with a ruler.

“He found,” Klein pointed to the line, his words coming out in a rush,

“that the number of charges in the nucleus is strictly equal to its atomic number on the periodic table. Hydrogen is 1, Helium is 2, Lithium is 3… all the way to Bismuth’s 83.”

The air was suddenly quiet for a few seconds.

Adèle looked at the two of them blankly. “What… what does this mean?”

“It means the Creator God is a mathematician, and an obsessive-compulsive one at that.”

A smile, born of expectation, played on Lia’s lips.

“It means the nuclear model of the atom is absolutely correct.”

Klein took over, staring at Lia, his eyes burning.

“Before, we arranged the periodic table by atomic weight. But there were always a few elements whose positions didn’t match, whose properties were anomalous.

But now, if we arrange them by charge number, all anomalies disappear.”

He took a deep breath, as if to suppress the emotions surging in his chest.

“Lia, do you know what this means?

The properties of the elements, and even the chemical reactions of all things in this world, ultimately depend only on how many positive charges are in the nucleus, and how many electrons are arranged outside it.”

“The world has been simplified.”

Klein said softly. “Simplified into a few integers.”

Lia looked at Klein.

“Don’t get too excited,” Lia threw a bucket of cold water on his enthusiasm.

“Although it’s warm water. The ‘grand framework’ is correct, but the renovations aren’t finished yet. Henry’s experiment only proves that our foundation is solid, but the house is still drafty.”

“Drafty?”

Adèle pointed downstairs. “From the looks of it, they’re about to enshrine you in a temple.”

“That’s because they haven’t found the problem yet.” Lia stood up and brushed the cookie crumbs off her skirt.

***

As it turned out, Lia’s foresight was always annoyingly accurate.

Over the next three days, Klein’s mage tower was bombarded with an unprecedented level of trust.

The light of the teleportation array barely went out, and tons of experimental data flew into the study like snowflakes.

At first, it was all praise and confirmation.

“A great discovery!”

“The spectrum of the lithium atom perfectly matches the formula!”

“The doublet structure of the sodium atom has been partially explained!”

But gradually, as the precision of the experiments improved, some discordant notes began to appear.

***

Late on the fourth night, in the laboratory.

Klein was staring blankly at a precision spectrometer.

The room was lit only by the faint blue glow from the instrument’s core, illuminating his furrowed brow.

“It’s not right.”

He muttered under his breath, his fingers tapping unconsciously on the console.

“What’s not right?”

Lia was curled up on a nearby sofa, holding a book. She actually knew what was wrong, but she had to let Klein say it himself.

“The spectrum of the hydrogen atom.”

Klein turned around, pointing at the projection in the air. “According to your orbital model, when an electron jumps from the third layer to the second, it should emit a red light of a specific frequency. One line. A single, pure red line.”

Lia nodded.

“Theoretically, yes.”

“But in reality, it’s not.”

Klein waved his hand, and the projection was magnified. Under extremely high magnification, the red spectral line had actually split into two, or even more, very closely spaced fine lines.

“It’s split.” Klein’s voice became a bit hoarse. “It’s like thinking someone is a bachelor, but when you get closer, you find out he actually has a whole family.”

Lia almost burst out laughing and quickly covered her face with her book.

“A very vivid description.”

“That’s not even the worst part.”

Klein walked to the experiment table and activated a huge magnetic field generator.

A humming sound filled the room as a strong magnetic field enveloped the spectral tube.

“Look.”

Under the influence of the magnetic field, the already-split fine lines split again! One line became three, five, or even more. They were like ghosts dancing in the magnetic field, mocking the simple and elegant Bohr model.

“Why?”

Klein turned his head, his eyes full of confusion.

“If the electron is simply moving in a circular orbit, the energy should be singular. Why does the same energy level split when a magnetic field is applied? Does the electron have other motions in its orbit?”

Lia closed her book, her heart beating a little faster.

The Zeeman effect.

The Stark effect.

Fine structure.

The patches on the old quantum theory were wearing thin here.

The circular orbit model couldn’t explain these phenomena. It was necessary to introduce elliptical orbits, relativistic corrections, and even the concept that made classical physicists tear their hair out—spin.

But she couldn’t just say, “Hey, the electron is actually spinning on its own axis,” because in this world, no one could yet understand why a point particle with no volume could spin.

“Klein.”

Lia stood up and walked over to him.

She stretched out her hand and drew a circle in the air.

“Let’s do a thought experiment. If you’re skating on an ice rink,” Lia guided him softly, “you go around the rink in a circle. That’s one kind of motion. But what if, while you’re going in a circle, you’re also spinning in place?”

Klein’s pupils contracted sharply.

“Spin?”

“I didn’t say it was just spin.”

Lia shrugged, cunningly leaving some room for interpretation.

“I’m just saying, the electron’s degrees of freedom might be more than we imagined. It might not just have position as its only attribute. Perhaps it also carries some kind of… magnetism?”

Klein stood frozen.

His brain was working at high speed.

‘A rotating charged body will produce a magnetic field.’

‘If the electron itself is a tiny magnet, then when an external magnetic field is applied, its energy would of course be different depending on whether it’s aligned with or against the field!’

‘Different energy levels mean the spectrum of the emitted light during a transition will naturally split!’

“Dammit…”

Klein suddenly grabbed Lia’s shoulders, his grip so tight it made her wince. “How did you think of that? It’s… it’s sheer genius intuition!”

“Probably because I’m good at letting my mind wander?”

Lia blinked, trying to pull her shoulder free. “It hurts.”

Klein immediately let go, but the next second, he pulled her back into his arms, this time much more gently, but with a strength that brooked no refusal.

“Lia.”

His breath fanned across her forehead, carrying a hint of heat.

“I feel very scared right now.”

“Scared of what? That the edifice of your classical physics is about to completely collapse?”

“No.”

Klein shook his head, his arms tightening, imprisoning her against his chest.

“I’m scared of you. The things in your head are like oracles from another dimension. Every time you throw out an idea, the world is reshaped.

Sometimes I feel… you’re very far away from me, so far that I might never be able to catch up with your mental leaps.”

Lia was taken aback.

She could feel the deep-seated insecurity within this powerful man.

He was afraid. Afraid that she, this “anomaly,” would one day break free of his control and disappear beyond the shore of a truth he could not comprehend.

“Idiot.”

Lia sighed, wrapping her arms around his lean waist, her cheek resting on the robe on his chest, listening to the frantic beating of his heart.

“No matter how high an electron jumps, it can’t escape the gravitational field of the nucleus. Unless you, the ‘nucleus,’ decide to quit.”

Klein’s body stiffened for a moment, then softened.

He lowered his head, his chin resting on the top of her head, his voice low. “I will always be your ground state. No matter how high an energy level you’re excited to, you can only fall back to me.”

“Stop using physics terms to talk sweet, it’s weirdly cheesy.”

Lia grumbled, but her ears had quietly turned red. “Also, about that spectral splitting problem, there’s actually an even more troublesome explanation…”

“Shut up.”

Klein interrupted her.

“No physics tonight.”

He lifted her chin, his thumb gently caressing her lips.

“Tonight, we only talk about chemical reactions.”

“Huh? What kind of chemical reaction?”

“Guess.”

Outside the window, the lights of the Tower of Truth were still brightly lit.

Countless mages were tearing their hair out over the split spectral lines, trying to patch up the crumbling old model with complex mathematical formulas.

What they didn’t know was that in this small laboratory, a deeper revolution in quantum mechanics was quietly brewing in the intimate air.

And the fuse for this revolution was currently being kissed until she couldn’t breathe.