Lucian seemed to sense his teacher's mix of anticipation and exasperation, and handed over the paper with a smile. "It's a proposal attempting to explain His Excellency Chairman Douglas's speed-of-light experiment, along with the corresponding transformation equations. Nothing paradigm-shifting — it shares common ground with several hypotheses other Archanists have put forward."
This was the "Lorentz transformation" Lucian had prepared as a psychological warm-up for his teacher.
Fernando took the paper with a skeptical expression and began flipping through it. His face then became an indescribable kaleidoscope of emotions, leaving Lucian stunned. "Teacher, what's wrong?"
"Heh, heh." Fernando chuckled twice in succession. "This is the second time I've seen this paper in the past two months."
Lucian was mildly taken aback. "Another Archanist submitted a similar paper? How come I couldn't find it in the Archanist Review Committee's records? If I'd known someone had already proposed this, I wouldn't have written it."
Fernando temporarily set aside all the difficulties of "fission" and "fusion," reverting to his usual irreverent manner with a chuckle. "It's perfectly normal that you couldn't find it — he never dared to submit it. He just showed it to me privately and asked for my opinion."
"Which Archanist?" Lucian asked curiously, his surprise already mostly fading. It had been over three years since Chairman Douglas's speed-of-light experiment, and countless supporters of the wave theory were seeking wave-theory explanations for the experimental phenomenon — ones that had to incorporate Aether. It wasn't surprising that some Archanist had come up with something resembling the "Lorentz transformation."
Even though the mages of this world were repeatedly overturned by Lucian because so many things had yet to be discovered, their capacity for thinking was in no way inferior.
"It's Oliver. He started researching this problem three years ago after his bet with Florence, but the search for a new extra-dimensional space kept interrupting his thinking. It wasn't until the last few months that he completed the full set of transformation equations. He hypothesized that when an object moves relative to Aether, its length contracts along the direction of motion, thereby canceling out the differences in the speed of light from different directions and explaining Douglas's experiment. Your paper follows the same line, doesn't it?"
Fernando had only skimmed the beginning earlier, assuming that the derivation would inevitably lead to results similar to Oliver's paper, and hadn't actually read the whole thing.
Lucian nodded. "Yes, but why didn't His Excellency Oliver submit the paper?"
Even if he was too occupied researching the Dark Dragon God, he could have given the paper to his wife Florence or a student to submit on his behalf.
"Because he felt that the transformation equations still concealed many important things and couldn't explain why this phenomenon occurs. He had developed a new preliminary line of reasoning but couldn't carry the derivation through — he considered it absurd, incorrect, and contrary to reality. He's been seeking alternative directions, which is why he consulted me."
Fernando pursed his lips. "My view is that his thinking isn't clear enough yet — he wavers back and forth, to the point where even I can't tell what explanation he's really aiming for. I suggested he find some time to discuss it with you. You're the most paradigm-shifting, most open-minded Archanist around — perhaps you can help him find a new direction."
At this point, Fernando looked at Lucian with a half-smile. "I didn't expect you to have arrived at the same explanation. But I recall that you've always dismissed the existence of Aether — how could you suddenly use it as the foundation for explaining Douglas's experiment? Besides, there are problems within these equations, such as the length contraction of matter. I'm sure you can see them — there are serious issues. So, Lucian, what exactly are you trying to draw out by putting forward this paper?"
"I suspect you already have a deeper explanation, and you reverse-engineered this paper so that Archanists could accept it step by step. Come on — show me your real paper."
Looking into his teacher's vivid crimson eyes, which held both amusement and absolute seriousness, Lucian could only think: *My parents gave me life, but my teacher truly knows me.*
But should he really show his teacher Special Relativity just like that?
Seeing Lucian hesitate, Fernando glared at him. "What? You think I'm too stubborn and conservative, that my Cognitive World would collapse? After the energy quantum and the light quantum, what could possibly blow my mind? When you proposed the energy quantum hypothesis to explain blackbody radiation, I did lose control a bit, but I withstood it just fine, didn't I?"
*Teacher, that's just forgetting the pain once the wound heals.* Lucian still vividly remembered Fernando's fury, his despair, and the way he seemed to age before his eyes. But this was something he wouldn't dare repeat aloud — it would only bring down a terrifying roar.
After some thought, Lucian chose his words carefully. "I believe the change in length isn't a contraction of matter, but a contraction of space."
"A contraction of space... interesting. The precise definition of space will need to change..." Given the existing knowledge of spatial barriers, demiplanes, and spatial magic, Fernando didn't look particularly surprised. "Oliver had also considered moving in this direction..."
"Starting from Chairman Douglas's experiment, classical electromagnetic theory, and research on moving objects — and discarding Aether — one could propose a hypothesis: the constancy of the speed of light. That is, in different reference frames, the speed of light in a vacuum is absolute, and measurements always yield a constant value." Lucian went a step further, then explained the precise arcane definition of this hypothesis.
Fernando clenched his right fist and gently tapped it against his chin. "The constancy of the speed of light... With this hypothesis as a premise, many things could be derived... Just show me the paper."
Lucian quickly added, "There's one more prerequisite hypothesis: the principle of relativity. There are quite a few papers on this — you should have seen them, Teacher."
Mages frequently used sound-wave magic, and they had discovered that when an opponent was flying toward them versus fleeing away, casting a sonic boom spell produced noticeably different sounds — one sharp and hurried, the other stretched and drawn out. It appeared that the wavelength had changed, which was closely related to velocity. This had been discussed as a phenomenon illustrating the principle of relativity, and similarly, changes in the wavelengths of starlight had been observed as well.
Fernando nodded slightly, indicating his familiarity with these phenomena and theories. "Only two premises? That's very much in line with the theory you advocate — deriving a whole series of results from as few axioms and hypotheses as possible through logical deduction. Show me the paper. I'm mentally prepared."
"Teacher, why don't you derive His Excellency Oliver's transformation equations yourself based on these two premises? Assign the quantities introduced in the equations a completely new arcane significance, rather than leaving them as mere mathematical tools." Lucian made the suggestion.
Fernando said with some annoyance, "Fine — I want to see what conclusions can actually be drawn!"
He sat back down at his desk, picked up his Feather Pen, first listed the two premises, and then began re-deriving Oliver's transformation equations from them.
At first, everything went smoothly. A master Archanist like Fernando possessed such vast accumulated knowledge that he derived a whole array of equations with barely any deliberation.
As he wrote, Fernando's Feather Pen suddenly froze over the paper, unable to descend for a long time.
The black liquid at the tip of the pen gradually gathered into a tiny droplet, and under the influence of gravity, it detached from the nib, tracing a leisurely, elegant arc before landing on the paper and spreading into a small black stain.
Outside the magic tower, the Thunder Hell seemed to have suddenly intensified, as if roaring one furious blast after another.
Fernando raised his head, his vivid crimson eyes fixed on Lucian in shock, as though trying to confirm something.
Lucian didn't flinch in the slightest. Their gazes collided in midair, and there was an almost hallucinatory sound of sparks crackling.
Fernando took a deep breath, closed his eyes for a moment, then continued the derivation. Lines of equations appeared one after another, conclusion after conclusion emerged, and at some point, the study took on the indescribable sensation of space-time itself shifting.
The ruler, the Feather Pen, and the books all seemed to exhibit faint signs of contraction, and the ticking of the wall clock appeared to slow down ever so gradually.
Lucian closed his eyes and blocked his ears, relying solely on his spiritual sense to perceive — and realized that none of it was an illusion!
However, the changes were extraordinarily minute, imperceptible to any mage below the high-tier level.
This was the impact of his teacher's shifting Cognitive World upon the real world!
This was a Legendary Mage!
After an indeterminate amount of time, Fernando set down his Feather Pen and regarded the results of his derivation with earnest, focused attention. He let out a self-deprecating laugh. "I thought I had already gained a reasonable understanding of how the world works. But now I realize everything is so hazy — space and time are no longer what I originally imagined, no longer what they seem through direct perception. Heh — time turns out to be a function of velocity, dependent on matter itself. If I hadn't derived this myself, I'd have scolded you until you couldn't speak."
He raised his head, looked at Lucian, and spoke with utmost gravity. "These are conclusions derived from hypotheses. They need to be corroborated by actual phenomena; otherwise, this view of space-time of yours will remain nothing more than a hypothesis. Hmm — it can partially explain the phenomenon of starlight shifting toward the red end of the spectrum."
Fernando hadn't fully accepted it yet. Results obtained through logical deduction from axiomatic premises had to be empirically verified; otherwise, they were merely an elegant toy with no real significance.
"Some of the problems that have emerged with the artificial planets can be approached through time dilation. However, this theory is still incomplete — it doesn't account for the existence of gravity. It's only a preliminary explanation and is bound to have quite a few gaps."
Lucian produced some of the data he had gathered over the past few years, along with problems that Annick and Sprint had discovered. "...When using the cyclotron to accelerate particles, deviations between actual results and theoretical predictions appeared. But introducing the relativistic framework provides an excellent explanation: mass increases as velocity increases, which in turn alters the orbital period. We can use this formula to calculate the magnitude of the change, then adjust the frequency of the electric field's oscillation. If the particles can be accelerated again without escaping the electric field, it would serve as indirect proof of the existence of relativistic effects."
Fernando was a man of action. He immediately began calculating, then opened up the magic laboratory and activated the cyclotron. Once the velocity reached a certain threshold, he continuously adjusted the oscillation frequency of the electric field.
After a while, Fernando obtained particles with energy exceeding that of any previous experiment. He sighed softly. "Lucian, in your 'Voice of the Mysteries,' you proposed the concepts of worldview, philosophy of life, and values. In my view, 'worldview' is equivalent to one's understanding of the world — and aside from the humanistic and historical content, it's essentially the same as the Cognitive World."
Lucian wasn't sure why his teacher was bringing this up and felt momentarily confused.
Fernando chuckled. "And one's view of space-time doesn't exist solely within the Cognitive World — it's also reflected in one's philosophy of life and values. So, your Legendary class might as well be an entirely new one, called the 'Destructor of the Three Worldviews.'"
"Teacher, now is not the time for jokes..." Lucian said, embarrassed.
Fernando regarded Lucian with that enigmatic half-smile of his. "If I hadn't endured the paradigm-shifting shocks you've brought several times over and started approaching every theory with a degree of skepticism, I probably wouldn't have been able to handle this."
"What you've named 'Incomplete Relativity' must be released gradually. You especially can't let Douglas see it all at once — it's a massive overturning of his entire theoretical framework. After enduring the blows from the wave theory of light and the challenge to continuity posed by quantum theory over the past one or two centuries, I seriously doubt he could withstand this one as well. It probably wouldn't cause his head to literally explode or destroy a demiplane, but he might end up like Brooke — and psychologically, there could be other changes as well..."
"Teacher, I never intended to reveal it directly — you insisted on seeing it," Lucian protested.
The longer he spent with his teacher, the more Lucian's casually spirited side surfaced unawares.
Fernando pretended not to have heard. "I'll start with Oliver. Since he's already identified the problem, he should be able to accept it. Then I'll have him release his paper to provoke thought among the high-tier and above mages."
"Why only high-tier mages and above?" Lucian asked, slightly puzzled.
Fernando dropped his serious expression and grinned. "You think the ones below high-tier could understand it?"
He shut down the laboratory and returned to the study, muttering as he walked. "Your arcane points are already at the seventh level, and the debate between light quanta and wave theory is still ongoing. Once the new alchemy citations start feeding back, combined with the gains from this paper, reaching the eighth level shouldn't be difficult. However, all you need is to discover the neutron, or complete this paper, and you can receive the Grand Archanist title directly. Points don't hold much meaning for you anymore — focus on improving your arcane strength. The possession incident involving the Silver Moon and the Undead Realm entity should have yielded you considerable gains, and the Council's resources will now be fully directed toward you."
Lucian currently had just over fifteen thousand arcane points — still half away from the eighth level. But the citation feedback from new alchemy was sure to be unimaginably generous.
When they arrived at the study, Fernando handed the paper back to Lucian. "Check if anything is missing. If it's all there, I won't need to see your original paper."