He changed Tiwat

"The key point is that, according to the logic of 'determinism,' the movement of these microscopic particles is also arranged by 'fate.' After all, everything composed of these microscopic particles should operate according to a 'preordained' pattern. It's like how you can't see every single hair in your body, but you can make your hair sway with the movement of your head."

Mona gently combed her braid that fell to her chest. The strands of hair parted smoothly with the movement of her fingertips, and the feel was no different from usual.

But Mona had a vague feeling that something was different—a premonition that "the big one is coming."

Han Fulai continued, "However, when scholars in my world studied microscopic particles, they discovered that they possess some wondrous properties that cannot be understood by common sense."

"For example, humans cannot accurately measure the position and velocity of a microscopic particle simultaneously. It's like we can accurately know that a person's height is 170 centimeters, but his weight varies greatly each time it is measured. The first measurement will show 50 kilograms, but the second measurement will show 50 tons... It is generally believed that this is because human observation affects the state of the particle."

"For example, light is both a particle and a wave. We have a famous 'double-slit interference experiment': when a beam of light passes through two parallel slits, it will appear as stripes of light and dark on a piece of cardboard behind the slits, showing the ripple characteristics of water waves; but if we install a phonograph behind one of the slits to observe the state of the light as it passes through the slit, it will obediently turn into individual particles."

"If conditions permit, we can actually reproduce the 'double-slit interference experiment' mentioned above in your laboratory. The experimental conditions are not complicated, and I still remember how to do it..."

Han Fulai was a little guilty when he said this. The "double-slit interference" experiment is indeed very simple and can be done at home by physics enthusiasts. It is introduced in various popular science books. However, he had never done such an experiment on Teyvat. What if the physical laws here are different from those on Earth?

However, based on his life experiences since his transmigration, as well as the various "coincidences" he discovered in Liyue and Mondstadt that are related to Earth's culture, he believes there is a high probability that quantum mechanics will work in this world as well.

He paused, then continued, "And the 'Schrödinger's cat' thought experiment is the most famous example of it. In my world, this experiment uses a box containing radioactive material, poison gas, and a cat."

"In short, a scientist named Schrödinger designed an experimental system in which there is a cat and a device that can release poison to kill the cat in a closed box. The probability of the device releasing the poison is random; it may or may not release it. So, when we open the box, we will see either a dead cat or a live cat, with a 50% probability of each."

"The question now is, if we don't open the box to look or peek in any other way, is the cat dead or alive?"

A huge question mark appeared above Mona's head—if this were a comic book, there would definitely be a question mark above her head that was even bigger than her head.

"Why ask such a question? The cat is either dead or alive, the chances are fifty-fifty." Mona made the first reaction that any rational human would have.

“But you can’t determine the cat’s current state without observing it,” Han Fulai coaxed. “Think about it, before you opened the box, what was the causal chain of this event that determined whether the cat lived or died, and what state the cat was in at that moment?”

Mona's brow furrowed even more: "The poison gas may or may not be released, the cat may or may not live... both dead and alive?"

Han Fulai smiled, “This is called ‘quantum superposition state,’ a cat that is ‘both dead and alive.’ But we know that we can never observe a cat that is both dead and alive. When you open the box, you can only ever see a living cat or a dead cat. That is, a cat that is ‘either dead or alive.’”

"...Are you trying to say that our observations...created the results of our observations?"

Mona rubbed her forehead vigorously, pondering this "Schrödinger's cat" problem repeatedly... Finally, she gave up thinking and asked directly: "So what exactly happened during our observation that forced a cat that was both dead and alive to choose between dying or living?"

Han Fulai shrugged: "I don't know. Nobody in our world really knows either. People call this phenomenon the 'observer effect,' which means that when our observations have an impact on reality, uncertain probabilities become certain."

"In short, the presence and consciousness of the observer can affect the state and behavior of the physical system, freeing the world from the 'fate' that could be written by 'Laplace's demon. Fate is no longer predetermined, because humans can change it."

Double Holiday Bounty Settlement

The Christmas and New Year's reward offer has ended.

As of today, the status is as follows.

Monthly tickets increased by 880, recommendation tickets increased by 1740, tips increased by 31800, and blades increased by 94.

According to the reward rules, this is equivalent to a total of 19 chapters, and we will start adding more chapters starting today.

Of course, it's impossible to pay it off in a few days. Survival is the priority, so I'll pay it off slowly.

I would like to express my special thanks to all the viewers who participated in the voting. This is the first time I have ever seen a monthly vote increase of hundreds in a single day.

Even though you guys don't usually talk much, it warms my heart to know you're all here when I vote. Thank you everyone!

I hope everyone will continue to support this book in the new year!

Chapter 257 I Am That Butterfly [4k]

Niels Bohr, the "father of quantum mechanics" on Earth, once famously said, "Anyone who doesn't get angry when he first hears quantum theory has never understood it."

Mona didn't get angry, which clearly shows she didn't really understand quantum mechanics.

Of course, this is also because Han Fulai, a liberal arts student, was not capable of helping Mona understand quantum mechanics.

Han Fulai did describe some perplexing phenomena in quantum mechanics to her, such as the so-called "observer effect," but Mona had never actually witnessed these amazing things firsthand. Thought experiments alone can only convey so much, so she was currently just confused.

She could accept that in Han Fulai's world, there was something called "quantum mechanics" that denied "predestination," but this was not Earth, but Teyvat.

Moreover, Mona has always been a straightforward person: "I can understand where your confidence in defying fate comes from... but what can 'quantum mechanics' help us do? Can it help us break 'fate' in this world as well?"

In fact, Han Fulai really wanted to reply to Mona with, "The Teyvat continent may not be without quantum mechanics."

There are many phenomena in Teyvat that are just as difficult to explain as quantum mechanics—for example, why can "willpower" become a force?

If Han Fulai were to explain it himself, he had a conjecture: Could "willpower" be some kind of "strong observer effect"? Could the "consciousness" of a large number of "observers" come together, interfering with macroscopic reality and thus changing the world?

Unfortunately, as a liberal arts student, his theoretical physics knowledge was limited to popular science books and was not particularly advanced. His research on these things could only go as far as "as long as the program can run."

However, he believes that with the development of science and technology, scholars around the world will one day be able to construct a theoretical framework for these things, just like quantum mechanics—provided that no one in the world throws a nail at their head.

He smiled and said, “Indeed, quantum mechanics is one of my sources of confidence. I also have another source of confidence, which is also my current guiding principle—for any matter, I now only ask two questions: First, should I do this? Second, can I do this?”

Han Fulai pointed to the top of his head once again.

"The one on Sky Isle is not qualified to be a 'Laplace's Demon' at all, nor can He control the fate of humanity and the world. He doesn't have that ability."

Mona's expression now showed genuine shock—Han Fulai's words just now were far more frightening than anything about "quantum mechanics," "Laplace's demon," "Schrödinger's cat," or the "observer effect."

This person just seemed to be saying that "Heavenly Principles" have no power to control human destiny? And they used a very disdainful tone?

Are all time travelers this awesome?

It wasn't until after the initial shock that she realized her living room had been enveloped in a pure white barrier, just like a few days ago, as Han Fulai had used the outdoor scene again.

—Although he says the harshest things, he does the most cowardly things. He even has to create a barrier to prevent the censors from seeing his insults behind people's backs.

This discovery made Mona burst out laughing.

Han Fulai calmly completed what he called a "cautious" operation, then pointed to his external barrier and said emphatically, "I'm not afraid of Him, I'm just explaining a principle to you. You see, even the ley lines have information that they can't grasp. Since He isn't 'omniscient,' how could He be 'omnipotent'?"

Mona reacted quickly: "But according to your theory, the so-called 'Laplace's Demon' only needs to know all the information about this world at a certain point in the past. What if He knew all the information about this world and arranged everything thousands or tens of thousands of years ago through the ley lines? Moreover... to the best of my knowledge, 'Destiny' has never changed."

For astrologers, the terrifying meaning of the "false heaven" is hard to describe in words; only the word "heavenly principle" can truly embody such power.

Whether fate is determined by a deity called "Heavenly Principles" or by the mysterious Heavenly Way, the terrifying power it represents is beyond the reach of mortals.

But Han Fulai had already anticipated Mona's reaction.

"Do you remember our previous definition of 'preordained destiny'?"

Mona nodded.

"Everything in nature, every 'cause' strictly determines every 'effect,' and every 'effect' can be traced back to its 'cause.' By extension, in the entire spacetime of nature, at every moment and at every location, all phenomena are strictly determined by the causal chain of natural laws. This is called 'determinism.'"

"And it was you, Mona, who gave me the inspiration to break the deadlock."

Han Fulai pointed at Mona.

Mona pointed to the tip of her nose, puzzled. "Me?"

Han Fulai nodded. "It's you. Your master is remarkable. The 'water divination' she taught you is actually no different from the way the person on Sky Island manipulates fate."

"Huh...?" Although Han Fulai had exaggerated their sect's "Water Divination Technique" to the level of the Heavenly Principle, Mona was secretly pleased, but she was more uneasy. She was the one who truly inherited the "Water Divination Technique," wasn't she? She wouldn't dare to boast like that!

“As we discussed before, the information you observe during divination is limited, and the results you deduce from that limited information are also limited.”

As Han Fulai spoke, he took out paper and pen from his pocket.

"The same applies to the laws of nature. Let's do a very simple prediction experiment. Mona, since you can calculate the trajectory of stars in the sky, calculating the trajectory of a simple ball shouldn't be difficult for you, right?"

He drew a rectangle on the paper that resembled a pool table, and then drew a small ball on the rectangular tabletop.

Then he marked two lines on the paper.

"A rectangular pool table, a small ball launched at two different angles, let's say the angle deviation is 5 degrees... Let's assume the ball's bounce has no energy loss or friction interference. After a period of time, say, after 10 bounces, Mona, can you draw the paths of these two balls?"

"This is just basic knowledge for astrologers." Mona pursed her lips and took the paper and pen without hesitation to mark the path for the two small balls.

Astrology is a standard science, and Mona can even calculate the trajectories of stars, so calculating the trajectory of a small ball is naturally a piece of cake for her. In terms of mathematical and scientific foundation, Mona's level might even surpass Han Fulai's.

The two small balls moved smoothly from Mona's pen tip, maintaining a very close parallel trajectory as they moved.

Han Fulai nodded again: "That's right. We generally believe that the more consistent the initial states are, the closer the future evolutionary paths will be. Two very similar initial states will have very similar future evolutionary paths. On this 'table,' small differences in initial conditions will result in very small differences in the paths. In our world, this is called 'system evolution is not sensitive to initial conditions.'"

"but……"

He picked up a pen and drew another table and a small ball, but this time, he changed the tabletop to a two-sided curved ping-pong table, similar to the shape of a sports field.

"Let's set the difference between the two paths at 5 degrees, or 10 bounces, genius astrologer, shall we calculate it again?"

"Hmm..." Mona looked at the pool table, hesitated for a moment, but quickly calculated the path of the ball.

This time, the paths are no longer like overlapping parallel lines; the two paths are almost completely opposite.

Han Fulai pointed to the two very different routes and stated his conclusion.

"We call this 'system evolution is sensitive to initial conditions.' The world we live in is such an extremely sensitive world. Two systems with very similar initial conditions can evolve on completely different paths in a very short period of time. These differences in initial conditions may be so small that we cannot distinguish them at all, but as long as there is a slight difference, it will lead to completely different evolutionary paths."

"It is precisely because the system is extremely sensitive to initial conditions that we need to know the initial state of the system with extreme precision in order to accurately predict its future. Otherwise, our prediction will completely fail in a very short time. Look at this ping-pong table on our paper. Just the change in the curvature of its edges has caused such a large difference in the predicted path. If we expand the prediction object to the entire world, how much more variables will we need to calculate?"

"Furthermore, since systematic errors are amplified at an exponential rate, this means that if we want to increase the length of time we can make effective predictions about the system, then we need to increase the accuracy by an order of magnitude for every second of prediction."

"For example... can the genius astrologer Mona accurately predict the weather in Mondstadt for a whole month?"

Mona shook her head decisively.

"...Although I don't know if the one in heaven can do it, I certainly can't."

Forget predicting the weather for a month, it's impossible to predict even a week. At sea, where the climate is even more complex, it's difficult to even predict the weather a few hours in advance—otherwise, the astrologers of the Ming School in the Church of Christ would have made a fortune by predicting the weather for fleets long ago.

Han Fulai smiled and said, "In my world, there's a very vivid metaphor to describe this: a 'butterfly storm.' In our terms, it means that if a wind-blown butterfly flaps its wings in a gust of wind, it will cause a storm on the Cloud Sea."

“‘Butterfly storm’…” Mona encountered another new term, but what intrigued her more was: “…Is your world so terrifying? Can a butterfly flapping its wings really cause a storm?”

Han Fulai laughed again, “I already said it’s a metaphor. The real meaning of this analogy is that if we want to accurately predict a storm two weeks from now, the information we need now must be as detailed as every tiny change, even as detailed as the wings of a butterfly.”

"Or, if we have two completely identical worlds, the only difference being that a butterfly in one world didn't flap its wings while in the other world flapped its wings, then two weeks later, the difference in weather between the two worlds will be macroscopic and disruptive. In our world, this theory is called 'chaos theory'."

“Chaos theory, hmm…that’s really interesting.” Mona’s eyes sparkled; she looked at Han Fulai as if he were a treasure trove.

She felt that she learned more from chatting with Han Fulai than she had from spending a year with the old woman—honestly, if she weren't worried about the old woman finding out she had been reading her diary, she would have already asked to join the "Liyue Academy of Arts".

She was even willing to forgo her salary, as long as Han Fulai could frequently consult with her about knowledge of the other world.

Han Fulai had no idea that the concepts he learned from popular science books almost helped Liyue recruit a genius astrologer for free. Quantum mechanics and chaos theory were just "Yan Kingdom maps" he used to lay the groundwork before explaining his true views.

After all this buildup, it's time to finally reveal the truth.

"Weather is a chaotic system full of countless variables, where even a tiny difference can lead to disruptive results."

"A chaotic system is one that, under conditions of extreme sensitivity to initial conditions, undergoes a fractal evolution of continuous self-replication, constantly mixing with its surroundings in a manner that tends towards infinity, and eventually inevitably diffuses into a huge space that we can no longer distinguish."

“Mona, think about it. If someone were to predict my actions for the week, they would have to take the weather around me into account. If it’s sunny today, I might go out; if it’s windy and rainy, I’d probably stay home. And each of us experiences countless weather changes in our lifetime, which adds countless variables to this prediction system.”

"Even if the Heavenly Principle determined the state of all systems in this world thousands of years ago, it has become completely unpredictable with the evolution of this chaos."

"In addition... on the continent of Teyvat now, there is the Traveler Luminous, and me."

Han Fulai finally put on his signature smile again.

"I am just one of the butterflies flapping its wings, a variable in the whole world."

"I see……"

Mona finally understood what Han Fulai was trying to say.

Because of the existence of quantum mechanics, the world has many more unpredictable "uncertainties"; because of the existence of chaos theory, even according to the rules of determinism, uncertain evolution can still occur.

In this world, there are already at least two butterflies that bring storms, butterflies that even Laplace's demon on the Isle of Sky could not predict.

Chapter 258 You Are the Observer (Bonus Chapter 1/19)

Today's conversation with Mona made Han Fulai see one thing clearly—why Wendy created that "meteorite shower." From this, he also vaguely discerned the reason why Tianli designed the "False Heaven," and the truth hidden behind the "False Heaven."

Wendy's actions were not merely about revealing the truth to the "Trumans" trapped in the "theatre" of Teyvat, nor were they simply about making more people realize that they were "Trumans." Wendy's actions actually had a deeper purpose.

Just as Han Fulai said to Mona, the world should be a chaotic system. Whether it's the weather or the random behavior of each person, it should be something with huge and uncertain variables.

The exponential growth of errors in chaotic systems is a terrifying concept because its growth is on the order of magnitude, not just numerically.

It can amplify initial errors by orders of magnitude in a short period of time. For example, if the error doubles every second, then continuing this trend, it will amplify more than 1000 times in 10 seconds. This amplification speed means that an initial error as small as an atom can be magnified to the size of 1000 suns in just one minute!

But Tianli was able to construct a "false heaven" under such circumstances to control the fate of people all over the world... Don't be fooled by how confident Han Fulai was when he spoke to Mona before; he actually knew better than anyone how terrifying Tianli's power was.

As a veteran civil servant of the Sky Isle government, Wendy was naturally even more aware of this matter.

This is why Wendy created that "meteorite shower".

Although Han Fulai didn't know if Wendy had also heard of "chaos theory" from witches like Aerith who traveled everywhere, he understood what Wendy was trying to do—ultimately, Wendy was amplifying the "error" in the Teyvat "system".

The Heavenly Principle established the "False Heaven" and the ley line system, and set up the "Seven Governing Sovereigns of the Mortal Realm" for governance, dividing the Teyvat continent into seven countries, etc. These governance methods are actually quite ingenious - He gave a chaotic system a direction called "trend".

For example, it is very difficult for humans to control the movement of individual water molecules in a glass of water, and it is impossible to accurately predict the movement of each water molecule; however, as a whole "glass of water", we can very easily use fluid mechanics to predict its flow state.

For example, in history, the individual behavior of each person is random and completely unpredictable; but when all the people on Earth come together as a whole, the resulting grand history has very clear trends and patterns.