Chapter 148: The Photon’s Momentum

The mornings in the capital were always accompanied by the calls of street vendors, but not today.

In their place was the noise of owls flapping their wings.

Tens of thousands of owls clutched urgently printed journals, sweeping over the city skyline like squadrons of bombers.

In Klein’s mage tower.

Lia stuffed the last piece of bacon into her mouth and reached out to catch a gray owl flying in through the window.

It dropped a roll of parchment and cooed twice in a fawning manner.

Klein flicked a piece of shredded meat into its mouth.

The owl flew away contentedly.

Lia unrolled the parchment.

This was the latest special issue of the Journal of Magical Theory.

It featured her newly published paper.

“By the way, how many special issues has the Journal of Magical Theory put out for her now?”

“It’s out,” Lia said, wiping the grease from the corner of her mouth.

Klein sat across from her, holding a cup of coffee, his gaze fixed on that formula.

“This will be the straw that breaks the camel’s back.”

“Not the last straw,” Lia corrected. “This is just the first brick.”

She pointed at the formula.

“The particle faction now has a weapon.”

“Before, they only knew how to shout slogans. Now, they can do the math.”

“It’s the energy of the photon, the ransom for the electron, and what’s left is the kinetic energy of the electron escaping.”

“Simple subtraction.”

Klein set down his cup.

“Simple, and therefore fatal.”

It was indeed fatal.

By just one morning, the entire magical community in the capital had exploded.

The particle faction’s mages acted like fanatical believers who had received the holy scriptures.

They clutched this issue of the Journal of Magical Theory and stormed into every laboratory still clinging to the wave theory.

“Calculate!”

“Calculate for me!”

“Don’t give me any nonsense about wave vibrations—plug the data into this formula!”

“As long as you can calculate the electron’s kinetic energy, I’ll admit your wave theory is right!”

The wave faction’s mages retreated step by step.

They couldn’t calculate it.

The energy formula derived from wave theory deviated from the experimental data by a million miles.

But Lia’s formula nailed it every time.

Precise to three decimal places.

Data doesn’t lie.

On the plaza beneath the Tower of Truth, the two factions of mages clashed again.

This time, there was no large-scale magical bombardment.

The particle faction directly hauled a blackboard to the center of the plaza and scribbled data across it furiously.

The wave faction crowded around the edges, their faces ashen, unable to refute a single word.

“We’ve lost.”

In the underground laboratory of the Royal Academy of Magic, the atmosphere was so oppressive it made it hard to breathe.

Several old professors in gray robes sat around a round table.

The special issue of the Journal of Magical Theory lay in the center of the table.

“We can’t lose.”

The speaker was Bernard.

His eye sockets were sunken, his hair disheveled—he clearly hadn’t slept for days.

“The interference fringes are still there.”

“The diffraction is still there.”

“As long as those two phenomena persist, light must be a wave.”

“Lia’s formula… it’s just a coincidence.”

“Or some special property of waves we haven’t discovered yet.”

A young mage nearby spoke up weakly.

“But professor, that formula is too perfect.”

“Too perfect to be a coincidence.”

“Shut up!” Bernard slammed his palm on the table.

“Find a counterexample!”

“If the photoelectric effect can’t be explained, find something else!”

“I refuse to believe all light obeys that little girl’s words!”

In the corner.

A man who had been silent the whole time stood up.

He looked to be in his thirties, wearing thick-rimmed glasses, clutching a stack of freshly printed experimental reports.

Compton.

The rising star of the wave school, Professor Roentgen’s prized student.

“Where are you going?” Bernard asked.

“To do an experiment,” Compton said softly. The X-rays that his teacher Roentgen had discovered were showing some strange data lately.

“X-rays?” Bernard frowned. “That high-frequency wave?”

“Yes.”

Compton adjusted his glasses.

“If light is a wave, the wavelength after scattering should remain unchanged.”

“I’ll verify it.”

“As long as I prove the X-ray wavelength doesn’t change after scattering, Lia’s particle theory will collapse on its own.”

Bernard nodded.

“Go.”

“You’re our last hope.”

Three days later.

Compton locked himself in the laboratory, refusing to see anyone.

The lab was piled high with graphite blocks and photographic plates.

The air was thick with the smell of ozone.

Compton stared at the instrument in front of him.

It was a spectrometer he had modified himself.

The X-ray source was aimed at a graphite target.

The X-rays struck the free electrons in the graphite, then scattered.

According to wave theory.

The light wave strikes the electron, forcing it to vibrate and emit a secondary wave.

The frequency of this secondary wave should match the incident wave exactly.

Just like a water wave hitting a pier—the wave that goes around it keeps the same frequency.

Compton adjusted the angle.

Recorded the data.

Checked the plate.

His hand began to tremble.

There were two black lines on the plate.

One in the original position.

The other… shifted.

The wavelength had changed.

Impossible.

Compton clutched his hair, his nails digging into his scalp.

“The instrument’s broken.”

“It has to be the instrument.”

He disassembled the spectrometer, recalibrated it, and reassembled it.

Tested again.

Still two lines.

The line with the longer wavelength shifted farther as the scattering angle increased.

Compton slumped in his chair.

Wave theory couldn’t explain it.

If light were a wave, there was no reason for it to lengthen.

Unless…

His gaze fell on the copy of the Journal of Magical Theory in the corner of the desk.

Lia’s name on the cover stung his eyes.

That formula.

Compton swallowed hard.

With trembling hands, he flipped open the magazine.

“Light is particles—

bullets one by one…”

What if X-rays were treated as bullets?

Compton pulled out a fresh sheet of parchment.

He drew a circle on the paper, representing the electron.

Then an arrow, representing the photon.

Collision.

Like two balls on a billiard table.

The photon strikes the electron.

Transfers some energy to the electron.

The electron flies off.

The photon’s energy decreases.

With less energy E, the frequency ν decreases.

Lower frequency means longer wavelength.

Compton’s quill flew across the paper.

Conservation of momentum.

Conservation of energy.

He wrote out the system of equations.

Sweat dripped from his forehead onto the paper, smudging the ink.

But he didn’t bother to wipe it.

Half an hour later.

A formula for the wavelength shift appeared on the paper.

Compton stared at it intently.

He plugged in the scattering angle θ from his earlier experiment and calculated the wavelength shift.

Then he measured the distance of that offset black line on the plate.

Perfect match.

Thud.

The quill fell to the floor.

Compton felt the sky collapse.

He was a die-hard wave theorist.

He was the one meant to trample Lia’s fallacy underfoot.

But now, he had personally derived ironclad proof for the particle theory.

Light really had momentum.

Light really collided like little balls.

Lia was right.

Lia was actually right.

Compton covered his face and sat in the dim laboratory for a long time.

A knock came from the door.

“Compton? How’s it going?”

It was Bernard’s voice.

Laden with expectation, with anxiety.

“Did you find the counterexample? Tell those lunatics—light is a wave!”

Compton raised his head.

He looked at the data on the desk, then at the door.

If he burned this data.

If he claimed the experiment failed.

The wave faction could limp along a little longer.

But he was a mage.

Before becoming a wave theorist, he was first a mage in pursuit of truth.

Compton stood up.

Straightened his disheveled robe.

Picked up the parchment covered in formulas.

It was indeed betrayal.

But what he betrayed wasn’t truth—it was arrogance.

Compton opened the door.

Bernard stood in the doorway, watching him expectantly.

“Well?”

Compton took a deep breath.

And handed over the parchment.

“Professor.”

“We’ve lost.”

Bernard took the paper.

Glanced at it once, twice.

His face went from flushed to pale, then to ashen.

His hand went slack.

The parchment fluttered to the ground.

…

The next day.

The Journal of Magical Theory issued another special edition.

“Decisive Evidence for the Existence of Photons: They Have Momentum.”

In Klein’s high tower.

Lia folded the newspaper neatly and set it aside.

“Faster than I imagined.”

Klein was tinkering with a new alchemical instrument.

“Compton’s an honest man.”

“Also a smart one,” Lia said. He knew he couldn’t hold it back.

“Does the wave faction have nothing left to say now?” Adèle poked her head out from behind a pile of test tubes.

“Not yet.”

Lia shook her head. “They still have interference and diffraction as their trump cards.”

“How do particles explain interference?” Adèle asked. “Two bullets colliding can’t just vanish, right?”

“We’ll talk about it later.”

Lia didn’t want to unleash probability waves just yet.

That was the most counterintuitive—and maddening—part of quantum mechanics.

These mages had just accepted light as particles; they needed time to digest it.

Otherwise, St. Mungo’s Hospital really would run out of beds.

Though the necromancy faction might be thrilled to death.