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Join the ServerThe debate ended in discord.
The academic circles of the capital, far from finding clarity after this confrontation, plunged into an even deeper fog.
The opposition between the Particle School and the Wave School spread from the conference rooms of the Tower of Truth to the classrooms of the magic academies, and even to the taverns in the streets.
Supporters attacked each other, and some who were once friends became enemies over theoretical disagreements.
It was as if the pause button had been pressed on all of theoretical physics in the magical world.
Amidst this chaos, the morale of the Particle School hit rock bottom.
Victor’s “symphony” speech echoed in the mind of every member of the Particle School.
They had won the confrontation of data but lost the beauty and completeness of theory.
They were like a group of beggars clutching gold nuggets, rich yet devoid of all dignity.
As their leader, Henry bore the greatest pressure.
He locked himself in his private laboratory, refusing all visitors.
Inside the laboratory, piles of experimental reports and calculation manuscripts were stacked high.
On one side was the impeccably precise data from the photoelectric effect and Compton scattering, which clearly screamed, “I am a particle.”
On the other side were the elegant and harmonious concentric circles of electron diffraction, which gently whispered, “I am a wave.”
These two voices warred violently in his mind, threatening to tear his spirit apart.
He had tried to construct new models, attempting to incorporate wave properties into the framework of particles.
He hypothesized that particles would periodically “pulsate” as they moved, thereby producing wave-like effects.
But all his calculations ultimately led to self-contradictory results.
He had also tried to attack the wave theory.
He worked through the night, trying to prove that the “wave packet” was mathematically unstable, that it would dissipate over time and could not maintain a particle-like form at all.
He succeeded.
But this proof was meaningless.
Victor could easily brush it aside with the “special nature of the microscopic world.”
Without more solid evidence, it was all just a futile war of words.
The days passed, one by one.
Henry grew more and more haggard.
His bedroom and study were filled with discarded drafts from the laboratory.
His eye sockets were sunken, his face unshaven, and his entire body had thinned considerably, leaving only a pair of bloodshot eyes that still flickered with a stubborn, unquenchable light.
He felt like he had walked into a dead end.
Despair, like icy seawater, was slowly drowning him.
Late one night, an exhausted Henry leaned back in his chair, intending to rest for a moment.
His gaze unintentionally swept over a pile of forgotten old journals on the corner of his desk.
The one on top was an issue of “Magus Theory” from several years ago.
The title on the cover made his heart skip a beat.
“An Empirical Formula for the Law of Black-Body Radiation.”
Henry picked up the journal.
He knew this formula, of course.
A monster forcibly pieced together to fit the experimental data.
In the low-frequency region, it behaved like Rayleigh’s formula.
In the high-frequency region, it behaved like Wien’s formula.
It perfectly solved the “ultraviolet catastrophe” and was mathematically flawless.
But everyone believed it held no physical meaning.
It was just… a tool that happened to work by coincidence.
Planck himself had called it “a fortunate guess.”
Henry looked at this formula, and on a whim, he recalled the paper on the “energy quantum” that Professor Lia Farrien had published even earlier.
‘Energy… comes in discrete portions.’
At the time, the entire magical world had considered it madness.
But it was this very “madness” that perfectly explained the photoelectric effect.
A thought, like a bolt of lightning on a dark, rainy night, struck Henry’s chaotic mind without warning.
What if…
What if Planck wasn’t just “piecing things together”?
What if, behind this formula, lay a deeper law, one originating from the very essence of the world?
What if the nature of black-body radiation, a purely thermal phenomenon, was also related to the particle nature of light?
This idea was so insane, so heretical.
Black-body radiation belonged to the realm of thermodynamics, the classical doctrine of continuous energy transfer and distribution.
And the light quantum was heresy belonging to optics, to the domain of electromagnetism.
To connect them?
That was more absurd than asking an elemental mage to study necromancy.
But Henry had been forced to the edge of a cliff.
He had no other path to take.
Even if there was only a one-in-ten-thousand chance, he had to seize it.
He shot up from his chair and rushed to the blackboard.
The fire in his eyes had reignited.
He began to construct an entirely new model.
Assume a closed cavity at a specific temperature.
Its inner walls are composed of countless tiny “harmonic oscillators.”
These oscillators can absorb and radiate electromagnetic waves.
According to Professor Lia’s theory, the energy absorbed and radiated by these oscillators is not continuous, but comes in discrete packets, with each packet of energy being an integer multiple of hν.
Now, the crucial question arose.
What about the electromagnetic waves within the cavity, the things we call “light”?
Henry made an even bolder assumption.
Assume that this light is also composed of countless independent, indivisible packets of energy.
Each energy packet is a “light quantum,” and their energy is hν.
The entire cavity thus becomes a container filled with a “gas of light quanta.”
Now, what he had to do was use statistical methods to calculate how the energy of this “gas of light quanta” would be distributed according to frequency at thermal equilibrium.
This was a territory no one had ever set foot in before.
He had no formulas to reference, no literature to consult.
He had only the most basic principles of statistics and that insane “light quantum” hypothesis.
He began to derive furiously, calculating the number of particles in different energy states, the total energy of the system, the entropy.
His chalk flew across the blackboard, making a “shh, shh” sound, the only sound in the entire laboratory.
Manuscripts piled up on the floor.
Failure after failure.
Starting over, again and again.
Time lost all meaning in his world.
He forgot hunger, forgot fatigue, forgot the rising and setting of the sun and moon outside his window.
His entire world was reduced to those dancing symbols and that distant, hazy goal.
He didn’t know how much time had passed.
Perhaps a week, perhaps two.
In the darkest hour before a new dawn, as Henry resolved the final integral and simplified all the terms…
He froze.
His hand stopped in mid-air, and the piece of chalk slipped from his fingers, falling silently to the floor and breaking in two.
On the blackboard, the final expression lay quietly.
Its form was completely identical to Planck’s empirical formula.
All the constants, C1 and C2, could be perfectly expressed using more fundamental physical constants—the speed of light c, Planck’s constant h, and the constant k.
He had succeeded.
He had actually, truly succeeded.
Starting from a purely statistical model of particles, containing no wave concepts whatsoever, he had, with irrefutable mathematical logic, perfectly derived the law of black-body radiation.
This was not a guess.
This was not a patchwork.
This was a logical proof, as solid as iron.
It proved that the particle nature of light could not only explain the photoelectric effect and Compton scattering.
It was also the underlying logic of the classic thermodynamic phenomenon of black-body radiation!
Henry stared blankly at the formula on the blackboard, his body trembling slightly from extreme excitement.
Then, he slowly began to smile.
He laughed softly at first, then the laughter grew louder and more unrestrained.
Finally, like a child, he roared with laughter in the laboratory filled with manuscripts.
That laughter was filled with long-suppressed exhaustion, grievances, and now, an incomparable ecstasy.
He had found it.
He had finally found a sword sharp enough.
He immediately rushed to his desk and spread out a fresh sheet of parchment.
He picked up his pen and, with a trembling hand, wrote a line for the title.
“Derivation of the Law of Black-Body Radiation from the Light Quantum Hypothesis.”
This paper would no longer be just another charge against the Wave School.
It would be a depth charge, aimed directly at the Wave School’s headquarters, a bombshell powerful enough to change the entire state of the war.
The entire academic world of the capital would be shaken by it.
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