*Thud, thud, thud.* Fernando, in his study, heard the gentle, rhythmic knocking on the door.
"So early?" Fernando stared at Lucian with his slightly bloodshot red eyes, his subconscious suddenly prickling with vigilance and wariness at the younger man's unusual behavior.
Lucian lowered his head with a smile. "I finished writing the paper just as the sun was rising, so I came straight here."
"What paper?" Fernando's sense of danger deepened—this wasn't some premonition from the Planet of Destiny, but rather the "crystallized wisdom" forged from too many encounters with the same pattern. "Is it subversive?"
Lucian considered for a moment, then nodded firmly. "It is, but it's based purely on observations from a large body of experimental results—there's no rigorous proof. It's entirely possible that in the future, another theory that encompasses these observational phenomena will overturn or subsume it."
"Let me see." Fernando breathed a slight sigh of relief. In that case, without conclusive evidence, no matter how subversive the theory was, it wouldn't make his head explode.
Lucian pulled out a paper and handed it over. The moment Fernando saw the title, his expression soured.
"«A Probabilistic Interpretation of the Wave Function.»" He read the paper's title word by word, a vague suspicion forming in his mind about its contents. Over the past while, the numerous electron scattering and diffraction experiments he'd conducted seemed to be pointing toward something, and the reality that
He flipped through the paper, reading in silence. The atmosphere around him grew increasingly oppressive, as though a storm of solid force was about to descend.
Suddenly, before he'd even finished, Fernando looked up. Countless sparks of lightning crackled through his red eyes as he spoke in an extraordinarily dangerous tone: "You're saying the wave function isn't a wave in the conventional sense, but a probability wave?"
Lucian met his teacher's perilous gaze without a shred of fear. "Yes. Based on observations of a large body of experimental results, and by incorporating Croy's statistical methods from the field of molecular motion, we can describe the wave function this way: it represents the probability of an electron appearing at a given position in space."
Fernando seemed to be suppressing a tremendous fury. "Then why does it have a definite position on the detection screen? The probability is a hundred percent!"
This was beyond dispute—every Archanist had seen the experiment in which electrons fired at a detection screen produced fluorescent dots. The position was definite, certain, and absolute.
Lucian understood his teacher's feelings and replied with great seriousness: "For instance, when we flip a coin without knowing the external conditions, throughout the process we can only say it has a certain probability of landing heads-up. But once it hits the ground, the outcome is already determined and won't change—the probability naturally becomes a hundred percent. What we're discussing is the electron *before* observation, not the electron *after* observation, when the outcome has already been fixed."
At this explanation, Fernando found it easier to grasp. His emotions eased slightly, and he seized on the key point. "Before observation? After observation? Then before we observe it, according to your interpretation, the electron could potentially appear at any position in space—it's just that certain locations have a higher probability?"
He simply couldn't fathom the electron's form of existence!
With coins, Fernando could accept it without any resistance—they alternated between heads and tails, which was why different landing outcomes were possible. But an electron? Because its description was based on spatial probability, it could be anywhere. Didn't that mean at any given moment it could be here *and* there simultaneously—that it was omnipresent?
That was more absurd and preposterous than any magic imaginable!
At least to date, setting aside the unknowable demigod tier, not a single magician had been able to create a spell that allowed them to exist in a similar state!
Lucian offered an analogy: "Before observation, the electron is like an insubstantial phantom cloud—it permeates space, omnipresent, a superposition of all possibilities. The denser regions correspond to positions where it's more likely to appear, but that doesn't mean it will necessarily appear there after observation."
"Before observation, the electron is something beyond our imagination—a contradictory yet unified monster possessing wave-particle duality. We cannot use our original concepts to envision its state; it would be meaningless. We can only describe it through experimental results that we can rigorously verify."
Fernando pressed his lips tightly together, as though opening them would unleash a roar.
Lucian pressed further: "In fact, you've surely observed this through arcane magic experiments—when we improve the Magic Circle and reduce the number of electrons fired at once, what appears first isn't a diffraction pattern but a chaotic scatter of detection dots. Only as the number of electrons increases does the diffraction pattern gradually emerge. Why is that?"
"That's because where a single electron ends up after diffraction is fundamentally unknowable—it's probability. We can only say it's more likely to appear *here*, which is why a small number of electrons produce a chaotic, random pattern. But once the quantity is large enough, the overall distribution conforms to probability: more electrons accumulate in some places, fewer in others, creating the alternating bright and dark bands of a diffraction pattern."
"It's like flipping a coin seven or eight times—we can't accurately predict how many times it will land heads-up. But once you've flipped it hundreds, thousands, or tens of thousands of times, the number of heads should be close to half!"
"If someday we could improve the Magic Circle to fire only a single electron at a time, the picture would become crystal clear."
"Probability, probability!" Fernando's expression twisted, as though he wanted to devour the very concept.
He didn't need Lucian to explain the basics of probability to him—this was one of the fields in which the great authority on thermodynamics was most knowledgeable and most skilled. And yet at this moment, the electron diffraction experiments he'd been conducting over the past while surfaced in his mind. Just as Lucian had described, when the number of electrons hadn't been large enough, the dots had indeed been chaotic and random.