Wizard of science

"Huh? Minus one-twelfth of a leaf." The devil was stunned.

Wei'er and Feier, who had been watching on the side, were also stunned after hearing this.

"What...what do you mean?" The devil felt that his brain was obviously confused and couldn't function properly.

"Let me explain the basic concepts first." Li He looked at the devil and said, "I'm not sure if you have the concept of negative numbers and fractions, but considering your performance in answering the questions just now, it's better to explain it clearly.

The first is the fraction. This is relatively simple. Divide an apple into two equal halves, and each halves of the apple are half, that is, 1/2. "

As Li He spoke, he took out a folding knife from his pocket and wrote the number 1/2 on the ground in Fonalense language.

After a pause, he drew a number line on the ground and continued: "As for negative numbers, we need to have a concept of a number axis. 0 is the center point of the number axis. Going to the right represents positive numbers, and going to the left represents negative numbers. -1 is opposite to 1. -2 is opposite to 2...

To understand it more simply, you can imagine that you have three apples... Well, that's not appropriate. You are a devil and you should prefer souls. Let's use souls as an example.

Imagine you have 3 collected fallen souls in your hand. One day you go to visit a devil friend, and as a meeting gift, you want to give him 4 souls. But you only have 3 in hand. After giving them all, you still owe 1. The 1 soul I owe is -1..."

devil:"……"

"Do you understand?" Li He finished explaining and looked at the devil to ask.

The devil didn't know why, but he had a feeling in his heart that he didn't want to look at Li He. He turned slightly sideways and squinted with a sullen face: "Of course I understand. How could such a simple thing trouble me? In fact... negative numbers, fractions, etc. Yes, it’s all in my memory, but I’ve been trapped for too long, my memory is damaged, and I need to take my time to remember it.”

"Is that so? That's best. Let's continue and increase the difficulty a little bit." Li He nodded lightly and continued talking without questioning the devil.

As he spoke, he kept writing on the ground with a knife: "Let's simplify the word problem just now into a formula. The first tree has one leaf, the second tree has two leaves... add up the leaves of countless trees, It should be: 1+2+3+4+..., we define it as S.

That is, S=1+2+3+4+5+6+……;

Then let S1=1-1+1-1+1-1+……;

1-S1=1-1+1-1+1-1+……=S1

So S1=1/2;

Then let S2=1-2+3-4+5-6+-……;

2S2=（1-2+3-4+5-6-……）+（0+1-2+3-4+5-6+-……）;

=1-1+1-1+1-1+……=S1;

So S2=S1/2=1/4;

Let S-S2=(1+2+3+4+5+6+……)-(1-2+3-4+5-6+……)

=0+4+0+8+0+12+0+…=4 (1+2+3+4+5+6+…)=4S

So S=(-1/3) S2=-1/12;

That is 1+2+3+4+5+6+……=-1/12. "

After the derivation, Li He put away his folding knife, looked at the devil, and said: "The derivation result can actually be simply explained as ζ(-1)=-1/12 in the sense of analytical continuation of the Riemann ζ function. In short, In the question I asked, the sum of the leaves of countless trees, or the sum of all natural numbers, is deduced to be -1/12. Do you understand?"

Devil: "..." Silence.

Continued silence.

There was a long silence.

The devil stared at the formula Li He wrote on the ground with a folding knife, and remained motionless and silent for a long time.

After a long time like this, the devil finally spoke up, his brows furrowed into a knot, and he shook his head repeatedly and questioned: "No, no, your answer is wrong. You are deceiving me.

Yes, you are cheating on me, you must be cheating on me. When countless leaves are added together, the number will only get bigger and bigger. How can the result become a fraction or a negative number? No, this is not right. "

"Isn't it right? What's wrong?" Li He asked slowly.

"This..." The devil paused, staring with big eyes, opening and closing his lips for a long time, "It's not right... it's not right..."

"What's wrong?" Li He asked again.

"Something's wrong..." the devil's voice became smaller.

"What's wrong?"

"No..." The devil's voice became inaudible.

"Actually, you are right, the answer -1/12 is indeed wrong." Li He suddenly said.

"Am I right?" The devil raised his head sharply and met Li He's gaze, his eyes a little unbelievable.

"Yes, you're right, that answer is wrong."

"Why?" asked the devil, the muscles on his face twitching uncontrollably.

"There are actually many mistakes and they are obvious." Li He said, "To give the simplest example, as I just said, the previous derivation results can simply explain the analytic continuation of the Riemann zeta function. (-1)=-1/12, so the = in 1+2+3+4+...=-1/12 cannot be recognized as = in the conventional sense at all, but refers to 'a certain function outside the definition domain' The value of extension = ', there are many attributes...

Let me talk about another key point. In the process of proving S1=1-1+1-1+...=1/2, one thing cannot be forgotten. S1 is a divergent series. As we all know, in infinite series, only absolutely convergent series can rearrange the terms without changing the converged values. Therefore, for the infinite series S1 that is not absolutely convergent, the summation order cannot be changed arbitrarily..."

"..." The devil's muscles on his face twitched more and more as he listened to Li He's words.

"...The step from S1 is wrong, and the subsequent derivation will naturally be meaningless." Li He finally concluded, paused and continued: "Actually, these words are for the second question I want to ask. The answer, but it doesn’t matter, let’s go directly to the third question.”

"The third question?" The devil was stunned for a moment, then asked with a straight face, "The third question, what is it?"

"The third question is also related to -1/12. ζ(-1)=-1/12 is a result in the sense of analytic continuation. It has no universality. In fact, its scope of application is very limited. It is generally used in mathematical number theory, engineering signal processing, physics string theory and quantum field theory. But in these fields, it is very important... The concepts of mathematical number theory, engineering, and physics are respectively...

Here, we focus on quantum field theory. The so-called quantum field theory is a set of self-consistent concepts and tools that combine quantum mechanics, special relativity and classical field theory. It is one of the important methods for studying high-energy physics. Many condensed matter physics problems can be solved using quantum field theory...

In quantum field theory, there is a very important definition called vacuum zero point energy, which is the energy contained in a vacuum and in the absence of matter. Under the classical physics system, it is generally believed that nothing exists in a vacuum and there is no energy. But in quantum field theory, it is believed that there are quantum fluctuations in the vacuum, and there is energy, which leads to spontaneous emission of atoms. Lamb shift and Casimir effect have confirmed this...

When quantum field theory calculates vacuum zero-point energy, it will encounter infinite results. In this case, it is necessary to use the ζ function and analytical continuation to deal with the divergence problem. After processing, the result is a bit ridiculous, it is 10^107 joules..."

What is the concept of 10^107 joules? Beyond anything known in the physical world. In other words, the entire universe combined cannot match this value. If this level of energy could be harnessed, even just a handful of it would contain enough energy to boil the entire world's oceans.

Li He looked at the devil, his expression gradually became serious, and he said seriously: "The third question I want to ask, and the real question I want to ask is, why is the value of the zero-point energy of vacuum so large, larger than the entire world?

What is the principle? Does the current magical power of the world play a role in this? Can spell powers be explained in quantum field theory?

Mr. Devil, you just said that you have extraordinary wisdom and terrifying power. As a being who possesses both magical power and excellent wisdom, and as a being from the mysterious hell, I think from your perspective, you should have a very good answer for me. So please give me an explanation - any explanation for these questions will do. "

"This..." After hearing Li He's question, the devil was stunned for a moment.

His expression was stiff, his eyes were wide and blank.

Sweat oozed from his face, and the muscles on his face were bunched up.

Like being petrified, he stood there, motionless and silent.

It's not possible to remain silent, because he... can't do this question at all!

"What, you can't answer it?" Li He said, "How about I change a few more questions? For example, in the sense of analytical continuation of the Riemann zeta function, ζ(-1)=-1/12 pairs of strings The importance of theory? The key to the verification of grand unified theory? Or the quantum decorrelation time extension method..."

"..." As Li He continued to talk, the devil couldn't help but raise his head and met Li He's gaze. For a moment, he felt his heart being pinched so hard that it became difficult to breathe. For some reason, he actually wanted to return to the Pampas Box.

He waited for a long time in the Pampas Box and thought about many possibilities after his release, but he never thought of this possibility.

"Why, you can't answer these?" Li He glanced at the devil and continued to ask, "Then why don't you answer something else, such as... quantum superposition state... Schrödinger's cat... quantum tunneling effect... …”

Devil: "..." He just wanted to be silent at this time, he didn't want to say anything, and he didn't want to think anything.

He felt that he didn't belong here at all, and that the Pampas Box was where he really should be.

But...he was released after all, and he stayed here after all.

So I could only listen to Li He continue to ask: "...What do you think the impact of dark matter on space should be?...What about dark energy..."

The devil felt extremely manic in his heart, but he did not dare to be manic at all.

He was scared now, very scared.

However, he had no idea what he was afraid of.

He only felt that he was not the devil, but the young man standing in front of him was.

No, the other party is scarier than the devil.

Because the other person is still talking.

"...What do you think is the truth about the Big Bang? In other words, what do you think is the truth about the birth of the world... Since you have extraordinary wisdom, even if your memory is incomplete, you should have some answers to these questions, right? …”

Finally, he collapsed.

he,

a devil,

Clenched his fists,

The eyes are red.

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