Lucian said with an innocent look: "I just got an idea from the remarkable result that electrons possess wave-like properties. I've revised and abandoned some of my previous thinking."
"Treating it as a wave to solve the orbit problem?" Fernando knew that would naturally lead to quantized orbits.
Lucian shook his head: "That approach might not fail to solve the problem, but I have other ideas. If that path proves fruitless, I can always come back to the wave perspective."
"Not from the electron-as-wave angle?" Fernando was always serious during Arcane discussions, and he couldn't quite fathom what else Lucian might deduce from this experimental result.
Lucian said with great earnestness: "It's from the conceptual thinking embedded in this phenomenon — what I've previously articulated as 'we can only rely on phenomena and results that are actually observable to deal with problems inside the atom.' We cannot let concepts that cannot be directly observed serve as foundations, such as orbits, just as we can only describe electrons as possessing both wave-like and particle-like properties."
"And then derive conclusions through mathematical tools?" Fernando said with considerable interest.
Lucian nodded lightly: "Yes. First, set aside the Arcane meaning of certain things, and use mathematical tools to link problems inside the atom with problems of the macroscopic world."
"Didn't you say we cannot simply equate the microscopic realm with the macroscopic world?" Fernando was a bit puzzled.
Lucian smiled: "That's exactly why we use mathematical methods. The microscopic world and the macroscopic world do indeed follow different rules, but when the rules of the microscopic world extend into the macroscopic world, observation results must be consistent with classical laws — otherwise we couldn't explain why all of us truly exist rather than becoming waves. So, for now, we set aside the Arcane implications of this change in laws, and use purely mathematical tools to construct a model similar to classical theory, one whose solutions match experimental results. Only then can we explore the model's actual significance."
"That is the most primitive and most classical approach, yet we've long forgotten about it." Fernando rarely let out such a remark. In the very beginning, when many concepts had yet to take shape, numerous theories were built precisely this way — starting from the results of exploring the world, constructing functions from experimental data, then discussing the actual meaning of those functions. But as theories multiplied and concepts accumulated, allowing Archanists to explore the world easily using established concepts and definitions, they also became correspondingly bound by them. "So where do you intend to start?"
Lucian made no attempt to hide his plans: "Naturally, I'll start from the sum of observable information about the internal atomic system — that is, from the overall state of the system. I'll introduce a state function, then treat observable Arcane concepts as operators to manipulate and transform the state function, yielding corresponding measurement results. These results must match experimental outcomes."
Fernando was silent for a moment, seemingly pondering the meaning of Lucian's words, before offering a rare compliment: "A remarkably novel idea — introducing state functions from thermodynamics into the internal atomic system, and treating observable Arcane concepts as operators. I'm afraid that kind of inspiration can only come from someone with a passion for pure mathematics. However, a cold, complex mathematical model ultimately must demonstrate its Arcane significance before it will be broadly accepted."
He didn't ask further about the specifics — that was Lucian's own work, unless Lucian chose to seek his guidance. "You've found a new way of thinking. You should be able to construct a theoretical framework fairly quickly. I hope it brings good news for my research."
"Master, what are you working on?" Lucian asked curiously.
Fernando said seriously: "Two directions. First, the anomalous Zeeman splitting experiments — I've found that it's necessary to introduce quantum numbers of one-half to resolve them, which contradicts the previous assumption that quantum numbers can only be integers. Second, I've gained some insight from past research, leading me to believe that no two electrons in an atom can be completely identical — meaning at least one of their quantum numbers must differ."
Three quantum numbers relating to electrons had already been discovered.
"This seems to offer a preliminary solution to the electron configuration problem, as well as the electron exchange problem in old alchemical reactions, providing some theoretical guidance for Mr. Gaston's research on life-matter synthesis." Lucian was quite surprised that his master had arrived at what amounted to the Pauli exclusion principle so quickly.
Fernando didn't appear pleased, but simply nodded: "The research is still a long way off. As you said, this is a realm that was previously beyond imagination. Besides, I'll be rotating into duty at the Netherworld forward base early next year."
Since the Lord of the Dead's rebellion in the Netherworld, the Council had established a base near the Netherworld rift at Heideler City to explore the realm. Because they suspected that the disappearances of legendary Mages such as Maskelyne and Vican were connected to the Netherworld, exploration was conducted with great caution. After several years, the forward base had only managed to push close to the depths of the Netherworld, and at any given time, a legendary Mage was stationed there — preferably a Grand Archanist. The war with the Church had been an exceptional case.
"You should be careful, Master," Lucian said with concern. The Netherworld was no less dangerous than the depths of the abyss, and when he had used his Supreme Council privileges to view Adol's memory visions, he had witnessed an unimaginable scene — profoundly shocking.
In Adol's memories, in a soundless, silent world, black, white, and gray enveloped everything. At the center of it all stood a magnificent black palace, large as half the Holm Kingdom, its towering spires reaching deep into the sky, deep into the void, as though connecting the heavens and earth of the Netherworld.
In the areas Adol could access, terrifying undead creatures were everywhere — ancient vampires and mummies, wraith lords, "Servants of Death" (a type of undead, not actual death gods), Skeleton Kings, dragon liches, and "demigod liches." The number of legendary-class beings was nearly equal to the combined total of the three great organizations. Fortunately, the vast majority of these undead had no intelligence and acted on instinct, making them difficult for the few sentient undead to command, so collectively they were still inferior to the Council itself.
Of course, the Council couldn't commit all its legendary power to exploration — that would give the Southern Church and the Northern Church an opening. Moreover, what horrors lurked in the deepest reaches of the Nether Temple, no one knew.
What shocked Lucian the most was the Soul Hearth inside the Nether Temple. It was located at the deepest point Adol could access — a gray curtain like a wall, hanging down from the unreachable highest point of the Nether Temple. Frozen within it were the faces of countless souls, their expressions shifting between serenity and torment, and on a few of them, white soul fire coiled and writhed.
These souls were densely packed, and Lucian suspected their number exceeded that of all sentient beings in the entire world.
Moreover, this Soul Hearth could only be touched by a handful of intelligent legendary undead who had received the favor of the mysterious existences of the Netherworld — allowing them to embed their subordinates within it and ignite the white flames to scour them. High-ranking undead including Adol could only see it, never touch it. It was the same feeling as when Mages advanced in rank, the same feeling as beholding a divinity sphere — lofty and remote, perpetually beyond their reach.
Adol had once studied the Soul Hearth carefully, only to spot his own face somewhere in the heights — he was already inside the Soul Hearth!
Even as an undead creature largely devoid of emotion, his mental force had trembled and his soul wavered, barely holding steady.
Perhaps the secrets of the soul lay hidden within. That was the only thought in Lucian's mind as he reviewed these records.
Fernando glared at Lucian with exasperation: "At the very least, only two or three of the legendary undead in the outer regions have reached the third tier of Legend. Communication methods have been established, and the mysterious Netherworld entities have fallen back into slumber. What danger could I possibly be in? Focus on your new alchemy model!"
After leaving his master, Lucian went directly to the Administrative Committee, while the discussion records from the meeting began circulating among a select few Archanists.