Dum, dum, dum. In his library, Fernando heard the slow door knocks.
“You’ve come so early?” Fernando gazed at Lucien with his slightly dirty, red eyes, with subconscious vigilance about his abnormality.
Lucien lowered his head and smiled. “When I finished the paper, it happened to be sunrise, so I went here straight away.”
“What paper?” Fernando had an even stronger sense of danger, which did not come from his Host Star of Destiny but from the multiple lessons in the past. “Is it disruptive?”
Lucien thought for a moment and nodded his head. “Yes. However, it is only based on the observation of tremendous experiment results and not strictly proved. The possibility can’t be ruled out that it will be disapproved or included by other theories that include those phenomena in the future.”
“Bring it here.” Fernando was relieved. In such a case, until decisive proofs appeared, even the most revolutionary theory could not blow up his head.
Lucien presented his paper, and Fernando looked awful after merely reading the title.
“‘A Probabilistic Explanation of the Wave Function’.” He read the title of the paper aloud one word after another and vaguely guessed what it was about. He somehow understood what the electron diffusion and diffraction experiments he worked on recently indicated, and why Oliver’s explanation of the wave function did not match certain experiment results.
Opening the paper, Fernando read on without a word. The atmosphere around was more and more depressing, as if a real storm was about to arrive.
Suddenly, he raised his head when he hadn’t finished the paper yet. With electricity flashing in his red eyes, he said dangerously, “Are you suggesting that the wave function is not a wave in the regular sense, but a wave of probabilities probability wave?”
Lucien looked back at his teacher’s dangerous eyes fearlessly. “Yes. By observing tremendous experiment results and introducing Chloe statistics in molecular movement, we can describe the wave function in such a way: it is an indication of the probability that the electron appears in a certain location.”
Fernando seemed to be holding his fury back. “But its location is fixed on the receiving screen. The probability is 100%!”
That was without a doubt. Every arcanist had seen the fluorescent points on the screen that were stimulated by the electrons. The undeniable experiment phenomenon suggested that the location of the electrons was absolutely certain.
Understanding his teacher’s mood very well, Lucien said solemnly, “It’s like when we toss a coin without knowing any external circumstances. During the whole process, we can say that the result may be heads and tails. However, by the time it hit the ground, the result will be determined, never to change anymore. Naturally, the probability is 100%. What we are discussing is the electron before observation, not the electron whose result has been determined after observation.”
Fernando found it easier to understand now. More or less eased, he grasped the key point. “Before observation? After observation? Then, according to your explanation, until we observe them, the electrons may appear in any location in space, except that the probability that it appears in some locations is higher than in others?”
He couldn’t imagine the electron’s form of existence at all now!
Fernando could accept the coin without any resistance, because it rolled in midair all the time, which entailed the different results when it hit the ground, but what about the electron? If the wave function described probabilities of location, the electron might appear anywhere. Did it mean that the electron might be in two places, or even all the places, at the same time?
That was more preposterous and unbelievable than any magic!
Up until so far, except for the demigods that he was unaware of, nobody could create such magic and let themselves exist in a similar form!
Lucien made an analogy. “Until we observe it, the electron is like an illusionary cloud that does not have any entity. It spreads throughout space and exists everywhere as a superposition of all possibilities. The thicker part of the cloud is the location where it is more likely to appear, but it doesn’t mean that the electron will surely appear there after observation.”
“Until we observe it, the electron is something we cannot imagine. It is a self-contradictory but unified monster with the wave-particle duality. Therefore, we cannot imagine its status with our original concepts, which is utterly meaningless. We can only describe it with the experiments that can be strictly verified.”
Fernando kept his mouth shut, as if he wouldn’t stop himself from roaring if he were to open it.
Lucien went further. “As a matter of fact, master, you must’ve observed that, after we modified the magic circles and reduced the number of electrons launched at one time, the first thing we would see was not the image of diffraction, but an assortment of messy fluorescent points. The image of diffraction only came into being when the number of electrons grew. Why was that?”
“It was because the destination of a single electron after it was diffracted was absolutely undeterminable; it was only a probability. Therefore, when electrons were too few, they would be disordered, but when there were enough of them, they would show the probabilistic distribution in general. There would be more electrons in some places and fewer in others. That’s how the image of diffraction was formed.”
“It’s like when we toss coins ten times, it’s impossible for us to predict how many times they are going to show heads, but if we toss coins hundreds and thousands of times, the times that they show heads should be half of the whole!”
“If one day we can modify the magic circle to the point that it can shoot only one electron at a time, the result will be even clearer.”
“Probability, probability!” Fernando’s face was so twisted as if he were going to eat probability.
He did not need Lucien to lecture him on the common sense of probability, which was one of the fields he was best at as an authority of thermodynamics. He remembered the electron diffraction experiments he did recently. It was true that the spots of light were messy until there were enough electrons.
Such a clear picture shivered his hands. A wind blew around him, turning the pages in the library with multiple loud noises. “Until they are observed, electrons are a cloud of probabilities spreading throughout space? After they are observed, they are matter with a fixed location? What happened during the observation?”
Lucien ignored the wind and spoke as calmly as if he were giving a death sentence. “The wave function collapsed. The overwhelming cloud of probabilities collapsed into a tiny spot with a fixed location. Observation caused the collapse of the wave function. As to what form the electron existed before the observation, it has nothing to do with us and is pointless!”
“Observation caused the collapse of the wave function?” Crack. A lightning struck the library and destroyed a statue. Fernando rose abruptly and glared at Lucien. “Our observation made the electrons change their form?”
Lucien nodded his head. “Master, what is our observation based on? We see things because of the reflected light, and we hear things because of the vibrations in the air. In the microscopic realm, even the slightest means of observation, like photons, will interfere with the electrons. That is to say, our observations on the microscopic particles will inevitably cause them to change.”
“The interaction of microscopic particles?” Fernando looked better and basically understood why observation caused the collapse of the wave function. As for the incomprehensible and unimaginable ‘cloud of probabilities’, he decided to leave it alone and focused on the key of Lucien’s explanation. “When we toss coins, we can predict the result correctly after learning all the external conditions, so it is not the real probability but a false probability. When there’s a cause, there’s a consequence. All the initial statues strictly and solely determine the final outcome. This is the foundation of the school of astrology and the foundation of magic!”
“Is the probability of the electrons also a false probability, because they are under the influence of the external conditions that we haven’t discovered yet?”
His voice was somewhat trembly, and more and more signs of a storm appeared in the library.
Lucien shook his head firmly. “At least so far, there are no phenomena that indicate the influence of external conditions. We can only say that probability wave is an intrinsic nature and quality of electrons!”
“Say again!” Fernando finally roared with a thunderstorm that created what appeared to be doomsday in the library.
Arcana and magic were so fascinating, and so many generations of sorcerers and arcanists devoted their talents and life to the exploration of the truth of the world, because they believed in the fundamental law of this world, under which everything operated strictly, like how the sun rose and set, how the celestial bodies moved, how it rained, and how elements reacted with each other. As long as they figured out the fundamental law, they would be able to grasp all the phenomena!
However, Lucien’s probabilistic explanation seemed to be laughing at their exploration, because the nature of the law of the world was ‘probabilities’? No matter how many rules and patterns they found, they could only predict that the odds that electrons appeared in this place were greatest but could not accurately describe where they would appear.
It had denied the foundation of the prophecy in the school of astrology, as well as the foundation of arcana and magic that explored the law of the world!
Pointing at the paper, Lucien looked at his roaring teacher solemnly. His Elemental Skin had been automatically triggered by the lightnings. “I have already put the conclusion in my paper.”
Fernando lowered his head and saw one part of the paper:
“In the past, everybody believed that, as long as all the factors at present were known, it would be able to rigorously infer, or determine, the result of an event. When there’s a cause, there will be a corresponding consequence, and vice versa. The arcanists respected the rule as determinism, or the law of causality.”
“I prefer a more strict definition. The real law of causality is the law of causality on the timeline. The cause must be before the consequence. Therefore, the previous law of causality should only be called determinism.”
“Now, what I want to say is that something may be wrong with determinism, because certain processes are probabilistic and irreversible…”
“Something is wrong with determinism and the law of causality?” Fernando glared at Lucien with his stormy eyes and roared amidst the thunders. “Are you telling me that the trajectory of the sun is probabilistic?”
BOOM!
“Are you telling me that our very existence is probabilistic?”
BOOM!
“Are you telling me that, even though we have constructed a magic model inside our soul and grasps its every detail, it will still be a probabilistic process when we perform magic?”
“Absurd! Ludicrous!”
BOOM!
In the rumbling thunderstorm, a vast universe appeared behind Lucien, in which the planets were made of protons and neutrons in different colors. The satellites around them, on the other hand, spread throughout the cosmos and existed everywhere, but when observed closely, they were fixed in one point.
BOOM!
The Thunder Hell mixed with the Atomic Universe, Lucien looked back at Fernando without wavering, before he said gravely:
“At the very least, determinism must die when it comes to the microscope!”
Crack. A thick bolt of lightning pierced out of the window and spread to the sky outside.
