Dum, dum, dum. Fernando heard the soft and slow knocks on the door in his library.
"So early?" Fernando stared at Lucien with his slightly dirty red eyes. He was suddenly alarmed by Lucien's abnormal behavior.
Lucien lowered his head and smiled. "The sun just rose when I finished the paper, so I came here directly."
"What paper?" Fernando had an even stronger sense of danger. It was not from the Host Star of Destiny but the crystallization of wisdom that had been condensed under the same circumstances many times. "Is it subversive?"
Lucien thought for a moment and nodded affirmatively. "Yes, but it's only based on the observations of a lot of experiments. There is no strict proof. It cannot be ruled out that it may be overthrown or covered by other theories that include the observations in the future."
"Give it to me." Fernando was relieved. In such a case, until there was no conclusive proof, even the most subversive theory could not make his head explode.
Lucien took out a paper and gave it to him. Fernando's face immediately turned gloomy after reading the title.
"'Probabilistic Interpretation of the Wave Function'." He read the title of the paper one word after another and vaguely guessed the content inside. The electron scattering and diffraction experiments that he had done recently seemed to be indicating something. The reality that Oliver's interpretation of the wave function did not match part of the experiment results seemed to be indicating something too.
Fernando opened the paper and read it without saying anything. The atmosphere around him was more and more oppressive, as if a substantial storm was about to arrive.
Suddenly, he raised his head, and electric sparks flashed in his red eyes. He said in an unusually dangerous tone, "Are you saying that the wave function is not a regular wave but a probabilistic wave?"
Lucien met his teacher's dangerous eyes fearlessly. "Yes. Based on the observation of a lot of experiments and the introduction of Chloe statistics in the field of molecular motion, we can describe the wave function in this way. It represents the probability that an electron appears in a certain location in space."
Fernando seemed to be holding back his fury. "But the electron has a definite location on the sensor screen. The probability is 100%!"
It was unquestionable. Every arcanist had seen the fluorescence spots caused by electrons when they were emitted to the sensor screen. It was an undeniable experiment, indicating that the position of electrons was certain.
Lucien could understand his teacher's feelings. He said solemnly, "For example, if we toss a coin without knowing the additional conditions, we can only say that it is likely to be heads up in the whole process, but when it hits the ground, the result has already been determined and will not change. Naturally, the probability is one hundred percent. We are talking about the electrons before observation, not the electrons whose results have been determined after observation."
With that said, Fernando understood better. He calmed down a little and grasped the main point. "Before observation? After observation? So before we observe it, according to your explanation, electrons can appear anywhere in space, but the probability of them appearing in certain places is higher? "
He couldn't imagine the existence of electrons at all!
Fernando was able to accept coins without any hindrance because they were constantly changing heads and tails. That was why they could land in different places. But what about electrons? Because the wave function described the probability of their position in space, they could appear anywhere. Didn't it mean that they could be here and there at the same time? They could be everywhere.
It was even more absurd and unbelievable than any magic!
At least so far, except for the unfathomable demigods, no sorcerer could create such a spell and allow themselves to exist in such a state!
Lucien made an analogy. "Before observation, electrons are like an illusionary cloud that does not have a real entity. They spread out in space and are everywhere. They are the superposition of all the possible states. The thicker places are the places where the probability of them appearing is higher, but it doesn't mean that they will definitely appear there after observation."
"Before observation, electrons are something that we cannot imagine. They are a contradictory and unified monster with the wave-particle duality. Therefore, we cannot imagine their state with the original concept, which is meaningless. We can only describe them from the experiment results that we can verify strictly."
Fernando closed his lips hard, as if he would roar if he opened his mouth.
Lucien went further and said, "As a matter of fact, master, you must've observed it through the magic experiments. After we modify the magic circles and reduce the number of electrons that are emitted at one time, we will see that the first thing that appears is not the diffraction image but the messy spots of light that electrons sense. As the number of electrons increases, the diffraction image is gradually formed. Why?"
"It's because it is impossible to know exactly where a single electron will appear after it is diffracted. It is a probability. We can only describe that it is more likely to appear here. Therefore, a small number of electrons will appear in a messy state, but when the number is large enough, the distribution of probability will be observed as a whole. There are more electrons in some places and fewer in some places. Therefore, the diffraction image will appear."
"It's like when we toss a coin seven or eight times, we cannot predict exactly how many times the coin will be heads, but when the coin is tossed hundreds, thousands, and tens of thousands of times, half of the coins will be heads!"
"If we can modify the magic circles to only emit one electron at a time, things will be even clearer."
"Probability! Probability!" Fernando's face was twisted, as if he were about to eat probability.
He did not need Lucien to explain the common sense of probability to him, which was one of the fields that he was best at as an authority of thermodynamics. At this moment, he recalled the electron diffraction experiments that he had done recently. Just like Lucien said, the spots of light were messy until there were not enough electrons.
Such a clear picture made his hands shiver slightly. A strong wind rose around him, making the papers in the library flutter. "Before the observation, the electron is a cloud of probability that permeates the space? After the observation, it is a matter with a definite location? What happened in the middle? "
Lucien ignored the wind and was as calm as the God of Death who pronounced the result. "The wave function collapsed. The diffuse cloud of probability collapsed into a tiny spot with a definite location. Observation caused the wave function to collapse. Before the observation, the form of the electron had nothing to do with us. It was meaningless!"
"Observation caused the wave function to collapse?" Crack. A bolt of lightning illuminated the library and destroyed a statue. Fernando stood up abruptly and stared at Lucien aggressively. "Our observation caused the electron to change its form?"
Lucien nodded. "Master, what is the basis of our observation? We see things because of the reflected light, and we hear because of the vibrations in the air. In the microscopic domain, even the slightest method of observation, such as photons, will cause disturbances to the electron. It means that our observation of microscopic particles will inevitably lead to their change. "
"The interaction of microscopic particles?" Fernando's face was more or less better. He basically understood why the observation caused the wave function to collapse. As for the incomprehensible and unimaginable 'cloud of probability', he decided to leave it aside for now and pointed at the core of Lucien's probabilistic explanation. "In the tossing of a coin, we can strictly predict the result of every toss by knowing the external conditions. Therefore, it is not a real probability but a pseudo probability. Where there is a cause, there is an effect. All the initial states strictly and uniquely determine the final result. It is the foundation of the school of astrology and the entire arcana and magic!"
"The probabilities of the electron are also pseudo probabilities. Are they affected by the external conditions that we haven't discovered yet?"
His voice was vaguely shivering. More and more signs of the coming storm appeared in the library.
Lucien shook his head firmly. "At the very least, there is no phenomenon that indicates the influence of external conditions so far. We can only say that the wave of probability is the intrinsic property of the electron!"
"Say that again!" Fernando finally roared. Lightning flashed and thunder rumbled, creating the scene of doomsday in the library.
The reason why arcana and magic were fascinating, and the reason why generations of sorcerers and arcanists sacrificed their youth, talents, and lives to explore the truth of the world was that they believed that there were fundamental laws in the world, and everything operated strictly under the control of the laws. For example, the sun rose and set, the celestial bodies moved, the wind and rain fell, the growth of creatures, the reactions of elements, the mysteries of matter, and the atomic structure. As long as they figured out the fundamental laws, they would be able to grasp them in practice!
However, right now, Lucien's probabilistic explanation seemed to be mocking such exploration, because the fundamental laws of the world were 'probabilities'? Even if they understood more laws of the world and reached the limits of life, they could only predict that the electron was most likely to appear here, but they could not precisely describe the location where it would appear.
It denied the foundation of the prediction of the school of astrology! It also denied the foundation of arcana and magic to explore the laws of the world!
Pointing at the paper, Lucien looked at his roaring teacher solemnly. Because of the spluttering lightning, his skin of elements had been naturally activated. "There are relevant explanations in the paper."
Fernando lowered his head and saw a paragraph in the paper:
"In the past, all of us believed that as long as we knew all the factors at present, we could deduce or decide the result of something strictly. What kind of cause leads to what kind of result, and such a process was reversible. That is to say, what kind of result leads to what kind of cause. The arcanists respectfully called it determinism, or the law of causality."
"I prefer a stricter definition. The real law of causality is the law of causality on the timeline. The cause must come before the effect. Therefore, the law of causality in the broad sense before is best called determinism."
"But right now, what I'm trying to say is that there might be something wrong with determinism here. Some processes are probabilistic and irreversible …"
"Something wrong with determinism? Something wrong with the law of causality? " Fernando stared at Lucien with storms in his eyes and roared in the rumbling thunder, "Tell me, is the trajectory of the sun probabilistic?"
BOOM!
"Tell me, is our existence probabilistic?"
BOOM!
"You're telling me that even if we've constructed a spell model in our soul and fully grasped every detail of it, and our spiritual power is in an abundant state, the process of casting a spell is still a process of probability?"
"Absurd! Absurd! "
Rumble!
In the middle of thunder and lightning, a vast universe appeared behind Lucien. The planets inside were made of protons and neutrons of different colors, and the satellites around them were everywhere in space. However, upon closer inspection, they were all in one place.
Rumble!
Mixed in the Thunder Hell and the Atomic Universe, Lucien looked at his teacher Fernando without flinching at all and said solemnly,
"At least in the microscopic domain, determinism must die!"
Crack. A thick bolt of lightning flashed across the window of the library and spread to the sky outside.
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