Chapter 141: The Birth of the Quanta

The night in the capital grew deep.

In the study on the top floor of the Mage Tower, only a single magical lamp remained lit.

The light was a pale white, illuminating the long table.

The table was piled with scrap paper and a dozen or so copies of this week’s journals.

Lia Farrien leaned against the back of her chair, clutching a newspaper in her hand.

The front-page headline was a line of bolded text: [Planck’s Formula: A Mathematical Coincidence or the End of Physics?]

Pinned beneath the newspaper was a letter.

It was from Augustus.

The principal of the Royal Academy of Magic asked her in the letter for her views on that “damned formula.”

He also mentioned that the current academy had turned into a total mess.

The mages of the Thermodynamic school were on the verge of madness.

They couldn’t explain why a formula that was essentially pieced together could perfectly fit all the data.

Some said it was a collective failure of the measuring instruments.

Some claimed that the Aether had undergone some unknown curvature at the microscopic level.

There was even an old man named Lorentz who tried to patch Rayleigh’s formula using electron theory; he calculated hundreds of pages of drafts and eventually calculated himself right into the hospital.

Lia tossed the newspaper back onto the table.

These people could rack their brains for an eternity and still never touch the core foundation.

Continuity.

This was common sense engraved into everyone’s very bones.

Just as water flows, wind is continuous, and mana is a smooth output.

No one would ever doubt this.

Lia picked up her quill.

The tip hovered over the ink bottle, hesitating to descend.

Once this thesis was sent out, it would be an earthquake.

Not just for physics.

The very theory of magic would be overturned along with it.

Traditional spell models were all built on the foundation of integrals and derivatives—that was the domain of continuous functions.

If she told those mages that mana was actually composed of individual particles…

She estimated quite a few people would suffer a complete collapse of their “path of the heart.”

Lia looked out the window.

The night sky was pitch black, with no stars in sight.

The laws governing the movement of stars in this world had already been set.

Now, it was the microscopic world’s turn.

Lia dipped the pen tip into the ink bottle.

She let it soak up the ink.

In the center of a brand-new sheet of parchment, she wrote down a title.

On the Theoretical Basis of the Law of Energy Distribution in the Normal Spectrum.

It was a very plain name.

Even a bit boring.

But the content inside would be incredibly provocative.

Lia started a new line.

“To all colleagues troubled by Planck’s formula:”

“Since Mr. Planck proposed his formula, I, like you, have been deeply fascinated.”

“I was also very curious about the meaning behind it.”

Lia wrote with great speed.

This feeling was quite wonderful.

In her past life, these theories were the golden rules in textbooks, the mandatory questions on exams.

Now, she was the person writing the answer on the blackboard.

“After several weeks of calculation and reflection, I have seen the dawn of a new light.”

“A completely unexpected sight has presented itself before me.”

Lia paused her writing and dipped her pen in ink again.

“The path we took before was wrong.”

“Merely introducing the kinetic theory of gases is completely insufficient.”

“In dealing with the relationship between entropy and probability, if we want our new equation to hold true, a certain assumption must be made.”

Lia’s wrist was steady.

Every letter was clear and powerful.

“Assume that when energy is emitted and absorbed, it is not continuous, but divided into discrete portions.”

Having finished this sentence, Lia placed her pen back on the rack.

She stared at that line of text.

In this world, this was the first time anyone had used words to express this concept.

Energy Quanta.

Lia picked up the pen again.

She drew several thick horizontal lines beneath the statement.

“To attract sufficient attention from every reader of this thesis, I believe I must repeat this passage once more, and I request the Association to make the font as large and bold as possible when printing the manuscript:”

Lia switched to a thick-nibbed quill and wrote forcefully:

“Assume that when energy is emitted and absorbed, it is not continuous, but divided into discrete portions.”

The ink seeped into the grain of the parchment.

It looked like a black scar.

“Perhaps some readers with less experience will have questions.”

“Energy isn’t continuous—what’s the big deal about that?”

Lia smiled to herself.

It was a very, very big deal.

“The answer is: it is a monumental matter.”

“Because it is the exact opposite of every concept we have held since the dawn of time.”

“From the ancient sages using magic to tame nature to the establishment of contemporary physics, every natural process has been treated by us as continuous and uninterrupted.”

After finishing this sentence, Lia fell into deep thought for a while, then stood up to stretch her stiff neck.

She paced around the room twice.

Walking to the bookshelf, she pulled out a copy of Introduction to Elementary Magic.

Flipping to the first page, it read: [Mana is like water, flowing endlessly.]

Lia closed the book and shoved it back.

From now on, this book would have to be rewritten.

Mana is like sand.

Lia sat back in her chair and continued writing.

“If your mentor told you that a carriage traveled in a straight line from Point A to Point B without passing through Point C in between, you would surely find it inconceivable.”

“Readers with a rich imagination might even suspect if said mentor has some nepotistic ties to the Principal of the National Academy of Magic.”

Lia blew on the wet ink.

Augustus would likely huff and puff when he saw this passage.

But the analogy was apt.

“The continuity of nature is so unquestionable that we almost never challenge it.”

“When a temperature needle rises from 20 degrees to 30 degrees, everyone will judge without hesitation that the temperature must have reached 25 degrees at some point in between.”

“28 degrees.”

“29 and a half degrees.”

“29.999 degrees…”

“In short, for any value between 20 and 30 degrees, as long as it is within that interval, the temperature must have been exactly equal to that value at some specific moment.”

Lia paused here.

She drew a thermometer on the edge of the paper.

Then she drew a cross over it.

“And the same applies to energy.”

“When we say a spell uses 100 units of mana, each of us subconsciously deduces that during the release of this mana, there was a moment when we consumed exactly 5 units.”

“3.14159 units of mana.”

“11.415 units of mana…”

“In short, the release of energy is continuous.”

“It always reaches any possible value within the range at some moment.”

“This concept seems like an absolute law of nature in the hearts of all of us.”

“However, in my research, I have found that Mr. Planck’s equation strictly requires that energy must possess only a finite number of possible states; it cannot be infinitely continuous.”

“When emitted, it must also be divided into finite portions; it must have a minimum unit.”

“Like an impoverished noble paying a bill with a heavy heart; although he tries to pay as little as possible, he must, regardless, pay at least one copper coin each time, because in terms of cash, there is no unit smaller than this.”

“This payment process is a discontinuous process; we cannot find any moment where this noble is in a state of having paid exactly half a copper coin, because the smallest unit is one copper coin.”

“We can find when he has paid 1 coin, and we can find when he has paid 2 coins, but between these two states, no other state exists—even though theoretically, there are infinite numbers between 1 and 2.”

“And I have discovered that the transmission of energy must also follow this currency-like method; it must transmit a specific amount at a time and cannot be subdivided infinitely.”

“Energy transmission must have a minimum fundamental unit. Energy can only be emitted in portions based on this unit, and situations like half a unit or a tenth of a unit cannot occur.”

“Between two units is a forbidden zone for energy; we will never find a measurement of energy that includes digits after a decimal point.”

Lia used a Mage’s Hand to bring a glass of cold water over and took a large gulp. Then, setting it aside, she picked up her quill to continue writing this thesis destined for greatness.

“And this fundamental unit, I shall tentatively call it the ‘Energy Quantum’.”

“The specific size of this minimum unit can be easily derived from Mr. Planck’s formula: it is equal to a constant multiplied by the frequency of the specific radiation, which can be expressed in a concise formula.”

Lia wrote down the specific calculation process.

She extracted that strange mathematical constant from Planck’s formula and endowed it with physical significance.

In this world, the “Joule” had just been defined during the glorious era a short while ago.

“Where E is the energy of a single quantum, v is the frequency, and h is the mysterious quantum constant.”

“Or, to commemorate the pioneer who fudged the formula despite not yet understanding the situation, we can call it the ‘Planck Constant’.”

(TN: Finally getting to the interesting physics)

📚 Also on NHV Novels

Evil Organization Executive, Forced to Become a Magical Girl

ComedyGender BenderGirlsLove

Read Now →
Not interested