Unfortunately, meeting Count Ludwig Everglow in person was impossible. An accident on the way could make me late for my thesis defense. Instead, we ended up speaking through letters...
Count Ludwig offered the following advice on how to prepare for a demonstration defense against a Great Mage.
[Avoid a direct confrontation if possible.]
"Hmm... I'm screwed."
[Great Mages can form an 'isolated system.' There is a qualitative difference between a mage who can do this and one who cannot.]
"Forming an isolated system?"
Could he be talking about the isolated system I know...? Nah, no way. It can't be.
A closed system, maybe, but a perfectly isolated system is impossible. The only 'truly isolated system' in existence is the universe as a whole. Besides, there was no way the people of this world, who didn't even properly understand thermodynamics, could distinguish between the two types of systems.
[Therefore, in this case, the standard response is to counter with long-range firepower to avoid being sucked into the system. Even if mana efficiency drops drastically, there's nothing better.]
"... It sounds like you're being serious."
What happens if I get sucked into the system? Unfortunately, Ludwig's letter didn't explain that part. It was more along the lines of, just assume you'll lose unconditionally if you get dragged in. ...
And so, with the truth still unknown, the day of the thesis defense arrived.
Outside the gates of the Imperial capital. The eastern district's Barren Mountain. There were no birds or flowers, but it was a truly beautiful day.
Yet even on a day like this, graduate students must be suffering... In the middle of a basin near the mountain's summit, a temporary spectator stand and dueling ground had been set up. Last night, the mages from some lab must have been cursing up a storm as they carried all the materials up here.
My sin is great. My apologies, colleagues. I looked around.
The Dean, Valerius, the princess, and numerous school heads. The most renowned mages of the Empire were all gathered. And in front of me stood Doloren and Giuseppe.
Giuseppe said to Doloren.
"Headmaster. Please go easy on him. Isaac is the future of our school."
"... I told you I know."
"..."
Giuseppe didn't seem to trust Doloren's words at all. A moment later, Giuseppe approached me.
"If you don't think you can do it, you can forfeit. You don't have to fight to the end."
"..."
Isn't it more common to cheer someone on, saying 'you can do it'? For Giuseppe to be like this, it meant this was no ordinary matter. A short while later, the thesis defense began with the Dean's opening declaration.
"As this data proves, when the temperature is constant, pressure and volume are inversely proportional, and when pressure is constant, volume and temperature are directly proportional. The basic framework of the 'ideal gas equation of state' I am proposing is a summary of these principles."
The audience nodded at my words. It would be hard to deny. Any mage with a bit of curiosity could prove my theory through experimentation.
This part had already been magically verified.
"According to this equation, as the temperature decreases, the volume of a gas decreases at a constant rate. So, what would happen if we continued to draw this graph?"
Doloren answered.
"At some point, the volume will become 0." "Correct. When the temperature reaches a certain point, the volume of a gas theoretically becomes 0. Using this temperature as a reference point, we can establish a universal standard."
Doloren smiled with her eyes.
"A very School of Magical Surveying-like approach."
"Thank you for the compliment."
"But I have a question. Is that temperature where the volume becomes 0 actually achievable?"
I answered immediately.
"It's impossible."
At my assertion, Doloren tilted her head.
"How can you be so certain?"
"Because as the volume of a gas approaches 0, the mana required to reduce it further approaches infinity."
"And this is coming from the man who used calculus to break down the boundary between an instant and infinity. Now you're saying infinity is impossible."
"..."
"There's no such thing as impossible in magic. Things called impossible are just lacking in either mana, affinity, or control."
"..."
Comparing the infinity of calculus with physical infinity. That's just sophistry. Doloren asked me again.
"And you still think it's impossible?"
"Yes."
"What's your reason for being so convinced?"
"Well..."
There was much to say, but I couldn't answer. No matter how brilliant a pianist is, you need a piano to play. And in this world, the 'pianos' known as 'thermodynamics' and 'quantum mechanics' did not yet exist.
At my silence, Doloren nodded.
"Right. Eventually, there comes a time when you have to stop answering. To prevent the infinite regression of language, someone has to draw a line."
"..."
"In that case, from now on, I'll ask with magic."
The smile vanished from her face.
"I propose a demonstration defense."
"... Are you asking me to prove the impossibility of absolute zero?"
"No. I will. I'm the opponent, after all. I believe 'absolute zero' is possible."
"... What?"
I understood that she was taking on the burden of proof.
But how?
No matter how great a mage Doloren was, what's impossible is impossible. At that moment, Valerius shouted in astonishment.
"Doloren! Surely, you don't intend to use that here?!"
The surroundings grew hectic.
"Damn... It seems she's really going to do it."
"Everyone, get ready! Begin the incantation!"
The school heads gathered together and began chanting a defensive spell, and even Valerius started muttering and preparing a spell of his own. I had a premonition that something terrible was about to happen. I needed to know what was going on to be able to respond.
So, as always, I started by employing a detection spell. Connecting my willpower to the mana field...
Connecting...?
Something was strange. The mana field itself was twisted. A grin spread across Doloren's face.
Doloren was at the center of the distortion. As if a rotating black hole were dragging space itself along with it, the mana field twisted and contorted around her. Suddenly, Count Ludwig's advice came to mind. -Therefore, in this case, the standard response is to counter with long-range firepower to avoid being sucked into the system. ...
I realized it too late. 'So this is an isolated system.' I had to escape.
F=ma.
I immediately launched myself toward the opposite peak. Fleeing any further was impossible. The mana field itself was so distorted that formulating a spell was incredibly difficult.
Doloren's figure had now shrunk to the size of my thumbnail. ... Would this be a safe enough distance? But even from so far away, Doloren's voice was crystal clear.
"Not nearly enough. If you were going to flee, you should have run beyond this mountain."
Like a whisper in my ear, without an echo.
"Isolated System Formation. Absolute Zero."
In that instant, my consciousness went black.
A mage who has reached a certain pinnacle develops a 'fervent wish'. This was a foregone conclusion from the moment humans, beings of infinite desire, were given mana, a wish-granting tool of omnipotence. But the laws of nature are more steadfast than magic and stand in the way of those wishes.
Thus, mages decided to create their own nature. A place cut off from the world, where they could project their own fervent wish. It was called an 'isolated system'.
It is said that the first Emperor of the Empire, who was the first to realize this, used an isolated system to banish the Dragon of Ruin from the world forever. And from the worldly singularity left behind by the first Emperor's 'isolated system', magical beasts from other dimensions still pour through.
That is the origin of the northern magical beast front. However, not every mage possesses such a clear 'fervent wish'. What kind of wish would a mage who was so beloved by mana that she became strong enough to kill a dragon at the age of ten, a mage who matured far too early, have?
What kind of isolated system would Doloren create? The Dean remembered. She remembered the isolated system she had seen during Doloren's promotion test to Great Mage.
There was nothing inside her isolated system. The Dean recalled her conversation with Doloren. -'Your fervent wish... is empty?' -'That way, when I find something I want to put in it, I can.' -'Hmm?' The Dean could only now understand Doloren's words.
"She meant she'd experiment with whatever she felt like."
A truly Doloren-like isolated system. As if in response to the Dean's words, Doloren spoke.
"Isolated System Formation. Absolute Zero."
The mana field, eroded by Doloren, swallowed an entire mountain whole.
I was standing in an unfamiliar space. The Barren Mountain was the same, but the sky had changed. The blue sky was gone, replaced by a sky of ash.
The only silver lining was that I wasn't alone under that sky. Giuseppe, Valerius, the Dean, and the rest of the school heads were all here with me. The school heads murmured.
"No sun, no moon, just gray."
"So this is the space that actualizes its own laws, the one I've only heard about in legends."
"But... it doesn't seem like much has changed."
As if answering their words, Doloren's lips parted.
"Within this space, in 'my magic', I shall assume that absolute zero is possible."
As she extended a hand toward me, a spherical 'something' formed in the central area between us. I reflexively cast a detection spell. The detection spell, now working properly again, gave me the answer.
The temperature inside that region was 0K.
Absolute zero.
It was qualitatively different from a vacuum with zero volume. Inside that area, all motion ceases. Thump, thump, thump.
My heart pounded fiercely with the intuition that a catastrophe was about to unfold. Soon, a bizarre phenomenon occurred in the absolute zero region. That part alone remained as a pitch-black void, as if a higher-dimensional being had cut out just that section.
It was stark black, with no outline or texture. I could hear people murmuring.
"What... what in the world is that? I can't see anything."
"The world has been severed."
"Even my mana detection isn't working."
The princess, her face pale, whispered to Valerius.
"Can... can something like that even be considered magic?"
Valerius replied with a grim expression.
"I do not know. This is not my fervent wish."
"..."
Among them, only the Dean maintained her composure. I stared again at that pitch-black, severed space. I had a rough idea of why the absolute zero space had become like that.
It was because bosons, like photons, had been annihilated due to the absolute zero temperature. However, strictly speaking, if a Bose-Einstein condensate were functioning properly, all the light should have become a single giant wave, affecting its surroundings in the form of heat. But that didn't happen.
By definition, that place was at absolute zero. There must be no heat. Because of that strange rule, the space became a bizarre black body that emitted no energy whatsoever.
"This is insane..."
Impossible things were happening one after another right before my eyes. A thermodynamic catastrophe. Its very existence was a violation of the laws.
Whoosh-!
Soon, a fierce wind began to rush toward the periphery of the absolute zero zone. With that as a start, the surroundings began to cool rapidly. It wasn't just the wind.
The moisture inside the Barren Mountain froze and expanded, shattering the mountain peaks.
Rumble-!
"It's... dangerous!"
"Quick, defensive magic!"
But the tragedy of us being crushed to death by a landslide did not occur. The flowing earth and rock moved around people on its own.
"W-we're saved."
At a school head's words, Doloren smiled sweetly and said.
"People don't die. That's the rule of this space."
"..."
It was hard to understand what that nonsense meant. But true to her words, my body heat wasn't being stolen at all. In fact, everyone within the isolated system remained completely unshaken by the winds rushing toward the absolute zero zone.
It seemed there was some kind of safety measure in place. But I had no idea what the principle behind it was. It was far too convenient.
Is something like this even possible with magic?
How?
Nevertheless, the absolute zero continued to create disaster. The air rushing toward the absolute zero point became denser the closer it got to the center. The light around it bent sharply.
Its periphery glowed faintly, like the sun's corona. It was an ultra-cold neutral plasma phenomenon. Seeing the sight, Doloren smiled brightly.
"Each one of those is a research topic for hundreds of years, right? You're truly amazing, Isaac!"
Doloren was delighted. They were all good research topics, it's true... But I couldn't just smile along.
I said to her.
"If this continues, we'll all die."
As soon as I finished speaking, the entire mountain range collapsed.
KABOOM! Rumble-!
This time, too, no one was hurt.
However.
The collapsed earth and rock followed the direction of the wind toward the absolute zero space. And the thousands of tons of debris that headed for the absolute zero space became a handful of black, degenerate matter.
"You'd normally only see something like that inside a neutron star..."
To see such a thing with my own eyes. It was astonishing. Of course, if I just stood here marveling, my own body might become one with 'that astonishing handful'. ...
And naturally, so would everyone else in this space. But Doloren still seemed perfectly calm.
She said.
"Don't worry. As I said before, people don't die."
I threw the words I heard during the thesis defense back at her.
"... How can you be so sure?"
Doloren answered immediately.
"Because I am beloved by mana. There's no way the conditions I set will collapse."
"..."
Are all Great Mages like this...? I don't think Valerius was like this.
Doloren said.
"If you doubt your safety, you're welcome to forfeit the demonstration defense."
"..."
"But if you do, you'll never see a sight like that again."
Doloren pointed to the absolute zero zone. To others, it might just be a disaster, but not to me. A black body that reflects no light.
Ultra-cold plasma. Degenerate matter. Bose-Einstein condensate.
'Where else would I get to see something like this with my own eyes?' To be honest, I wanted to study it a bit more. In my past life, I did it the way of a scientist; this time, I'd mix in magic.
I wanted to tear down that absurd magic.
"Feeling like fighting now?"
"Yes."
For starters... let's try anything. With all my strength. ∂u/∂t + u ⋅ ∇u = -1/ρ ∇p + ν∇²u + 1/3 ν∇(∇ ⋅ u) + g The wind was monstrously strong, but I managed to bring it under my control. And now, to pour energy into it.
E = hv The wind rushing toward the absolute zero zone now became a searing gale that would scorch anything it touched. It was a strike into which I poured hundreds of times more mana than the 'iron ball projectile'. Let's see if it can swallow this and still be fine.
'Please work...!'
The scorching hot wind surged toward the pitch-black realm of nothingness. But that was it. I expected a shockwave to erupt from the rapid density change, but not even a sound came from the absolute zero region.
"This is insane..."
Doloren replied to my curse.
"Looks like you did something interesting, but it seems to be useless."
"Dammit..."
I didn't give up and formulated another spell. This time, a vacuum. My plan was to isolate the absolute zero space by eliminating the very matter that exchanged heat.
But a problem arose from the spell formulation stage. The degenerate matter near the absolute zero point. I had no idea how to set up a calculation that included it as a variable.
I was certain that even old Richard Feynman himself wouldn't know. In the end, the calculation failure led to the collapse of the spell.
Fizzle!
"Kuh!"
The sensation of mana flowing backward and burning up washed over me. It was a rebound. It was over.
The laws were distorted, and my magic didn't work.
Whoooosh!
I could do nothing before the storm brought on by absolute zero. I think I've done all I can. ... Should I just postpone my master's for a semester?
That wouldn't be so bad. What's a master's degree anyway? At that moment, I heard Valerius's telepathy. -'It's too early to give up, disciple of Doloren.
Remember 'Achilles and the Tortoise'. Just like then, you must imprint your own fervent wish upon the world to fight back.'
Fervent wish?
What the hell is that? Soul, visualization, will, fervent wish, and so on... They're at it again with their otaku terms that only they understand.
But strangely, I found a hint in his words. Just like when I forced the concept of limits onto the paradox of Achilles and the Tortoise... It seems I can impose a law upon this entire space.
But I don't know what law I should impose. When even the cornerstone of physics, the laws of thermodynamics, has crumbled, what am I supposed to believe in? Then, I heard the Dean's telepathy.
'It doesn't have to be a phenomenon. Try establishing a rule you're most familiar with.' A familiar rule?
I don't know what that is... but strangely, one scene came to mind. I stared blankly at Doloren in front of me. A grin spread on her face.
"Giving up? Want to do your master's next time?"
"No. If I back down from a master's, how will I ever become a professor?"
"Then what will you do? Revise your thesis?"
Never in a million years. Because I just found the answer. Before entering graduate school.
I recalled a now distant memory. 'Why is this attached to the end of every problem?' -'... Without it, you'd die.' -'What?'
The practice problems I'd solved countless times from high school to my undergraduate years. The physics textbooks I'd read through the night. That one last line that appeared so often in every problem.
Perhaps the start of all my troubles was because 'that one line' completely disappeared in graduate school?
"Isolated System Formation."
I spoke 'that one line' towards the air surrounding the absolute zero.
"However, friction and air resistance are to be ignored."
Snap.
In that instant, the world went dark.