Chapter 220: A Patch and a Prophecy

Henry’s paper struck like a bolt from the blue, creating a tremendous uproar.

Copies of “The Journal of Magical Theory” were sold out within the next three days.

Countless mages and scholars, in their own laboratories or in the library of the Tower of Truth, repeated Henry’s derivation.

The expressions on their faces shifted from initial doubt, to astonishment midway through, and finally, to utter, disbelieving shock.

“He… he actually did it?”

“He derived the black-body radiation formula using a pure particle model?”

“How is that possible? This completely subverts the very foundations of thermodynamics!”

“This derivation… logically… is flawless.”

The camp of the Particle School erupted in celebration.

They ran around spreading the news, holding the special issue above their heads as if it were a banner of victory.

Overnight, Henry transformed from a tragic leader struggling to hold on into a hero who had turned the tide.

The Wave School, on the other hand, fell into a deathly silence.

Victor locked himself in his room, not saying a word.

As he read the suffocatingly rigorous derivation in the paper, he felt a chill from the bottom of his heart.

Henry’s counterattack was a hundred times fiercer than he had imagined.

This was no longer a confrontation of experimental data, but an escalation to the level of foundational theory construction.

Henry had proven that the particle model could also explain a classic phenomenon previously thought to belong to the domain of waves.

This made Victor’s assertion that “the world is purely made of waves” seem like a joke.

***

Meanwhile, in the study at the top of Klein’s mage tower, sunlight streamed through the massive floor-to-ceiling windows, spilling onto the carpet.

Lia sat cross-legged on the carpet, the controversial special issue of “The Journal of Magical Theory” spread open before her.

Klein sat on a nearby sofa, leisurely sipping his red tea.

“Mister Henry is truly impressive,” Klein said, putting down his teacup.

“To think of breaking through from this angle under such desperate circumstances… his perseverance and intuition are far beyond ordinary.”

Lia didn’t look up; her finger gently traced a line of statistical formula in the paper.

“Yes, it’s quite remarkable,” she replied softly.

“He has found the most solid theoretical cornerstone for the particle nature of light.”

“But…” Lia’s tone shifted.

“But?” Klein raised an eyebrow.

“But while his derivation’s result is correct, I found that the process itself is still flawed,” Lia said.

“Oh? Do tell, my dear honorary professor.” A corner of Klein’s mouth curved into an intrigued smile.

“He used the wrong statistical method,” Lia pointed out bluntly.

“He assumed these ‘light quanta’ are ‘distinguishable,’ like little balls each engraved with a different number.”

“Therefore, he followed the classical statistical method.”

“Although a few mathematical coincidences led him to the correct result in the end, the very logical starting point is wrong.”

Klein’s expression grew serious.

He was, of course, familiar with the statistical method Henry used; it was the foundation of statistical mechanics.

“What do you mean?”

“I mean that these ‘light quanta’ are identical, indistinguishable.” Lia looked up at Klein, her eyes clear and bright.

“You can’t label one photon ‘A’ and another ‘B’.”

“For microscopic particles, swapping the positions of any two identical particles does not cause any observable change in the entire system. Therefore, we should need a completely new statistical method to describe their behavior.”

Klein fell silent.

Lia’s words were somewhat beyond his current framework of knowledge.

‘Identical particles, indistinguishability…’ He had never heard of these concepts.

But his intuition told him that Lia was right.

This held a deeper secret about the fundamental nature of the world.

“Moreover,” Lia continued, “Henry’s model has another, deeper problem.”

“He didn’t explain why these light quanta, unlike electrons, do not obey the exclusion principle.”

“According to the exclusion principle, a single quantum state can hold at most one electron (with an opposite spin).”

“If light quanta also followed this rule, they would fill different energy states in sequence from low to high, just like electrons filling atomic shells.”

“The result calculated this way would be completely inconsistent with the experimental data for black-body radiation.”

Lia stood up and walked to the desk.

She spread out a sheet of parchment, picked up a quill, and dipped it in ink.

“So, we need to apply a patch to Henry’s theory.”

“A crucial one.”

Klein walked to her side, watching her quietly.

Lia didn’t hesitate, her quill flying across the page.

She first defined the concept of “identical particles” and, based on it, constructed a completely new statistical distribution model.

In this model, she discarded Henry’s assumption of distinguishing between particles in his statistics.

She treated all possible quantum states of the system as individual “rooms.”

And the indistinguishable “light quanta” were like nameless “tenants.”

What she needed to calculate was simply how many “tenants” were in each “room,” not which “tenant” occupied which “room.”

This new statistical method was far more concise than Henry’s derivation and more logically self-consistent.

It also perfectly derived the black-body radiation formula.

Next, at the end of the paper, Lia proposed a bold assertion.

“In summary, the fundamental particles of the universe appear to follow two completely different statistical laws.”

“One type, represented by electrons, is solitary, obeying the exclusion principle, with each one wanting to occupy a unique space.”

“The other type, represented by light quanta, is gregarious, not obeying the exclusion principle, allowing any number of particles to crowd into the same quantum state.”

Writing this, Lia paused for a moment.

An even more astonishing inference surfaced in her mind.

‘If the exclusion principle is invalid for light quanta, then…’

What would happen under certain extreme conditions?

She took a deep breath and, at the very end of the paper, wrote down the prophecy that would be enough to shock the entire magical world once again.

“Based on this property of light quanta, I hereby propose a theoretical prediction.”

“When we place a large number of light quanta in a closed system and lower its temperature to a sufficient degree, a peculiar phase transition will occur.”

“The vast majority of particles will abandon their chaotic motion at high energy states.”

“They will condense into the single lowest energy state, the ground state.”

“They will lose all their individuality, their behavior becoming like a perfectly synchronized legion.”

“Ultimately, they will form a giant quantum state that can be directly observed on a macroscopic scale.”

After writing the last word, Lia put down her quill.

She gently blew the ink dry on the parchment and handed it to Klein who was behind her.

“Perhaps this can be a congratulatory gift for Mister Henry,” she said softly.

Klein took the paper and read it word by word.

His breathing gradually quickened.

A completely new statistical method, a macroscopic quantum state…

Every word was like a powerful bomb, setting off tumultuous waves in his world of understanding.

He stared at the bold prophecy at the end of the paper, speechless for a long time.

Condensing innumerable particles into a single macroscopic quantum state?

This… this was simply the stuff of myths.

Klein’s voice was a bit hoarse, “Is there any experimental basis for this?”

“None at present,” Lia shook her head. “But theoretically, it must exist.”

Klein was silent for a long while.

Finally, he looked up at Lia, his blue eyes shimmering with a complex light.

“I’m beginning to think that everything you throw out is enough to send half the mages to St. Mungo’s Hospital.”

He carefully rolled up the paper and sealed it with a magical sigil.

“I imagine President Samuel will have another sleepless night when he sees this.”

This paper, titled “Supplementary Notes on Quantum Statistics and a Low-Temperature Prophecy,” was sent to the Magic Association under Lia’s name.

It did not cause a great stir immediately, unlike Henry’s paper.

Most people saw it as merely a footnote to Henry’s theory, a technical supplement.

And the prophecy at the end about a “condensed state” was dismissed by the vast majority of scholars, including supporters of the Particle School, as an impossible thought experiment.

The leader of the Wave School, Victor, even let out a disdainful sneer after seeing the paper.

“A condensed state? A macroscopic quantum state?”

“It’s the raving of a lunatic!”

He crumpled the paper into a ball and threw it into the wastebasket.

But for some reason, the term “condensed state” was like a thorn that had lodged itself deep in his heart.

A crazy plan began to form quietly in his mind.

He would personally use an experiment to expose this lie.

He would show everyone just how fragile the Particle School’s theory was in the face of reality.

He was going to sweep this so-called “condensed state,” along with the entire particle theory, completely into the dustbin of history.

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