Chapter 18: I can’t answer this question!
"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 glanced at the devil and said, "I'm not sure if you have the concept of negative numbers and fractions, but in view of your performance in answering the questions just now, it's better to explain it clearly. First of all, fractions,
this It's relatively simple. Divide an apple into two equal halves, and each halves of the apple are one-half, that is, 1/2." As he spoke,
Li He took out a folding knife from his pocket and used Fornalanza on the ground. Yu wrote down the number 1/2.
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, no, you are the devil, you should prefer the soul, so use the soul as an example. Imagine that you have
3 apples in your hand Collected fallen souls. One day you go to visit a devil friend. As a meeting gift, you want to give him 4 souls. But you only have 3 in your hand. After giving them all, you still owe 1. You owe this 1 soul is -1..."
Devil: "..."
"Do you understand?" After Li He explained, he looked at the devil and asked.
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 slowly remember it." "Well, 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
then S1=1/2;
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;
then 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 then
S = (-1/3) S2=-1/12;
that is, 1+2+3+4+5+6+...=-1/12." After the
derivation, Li He put away the folding knife and looked at the devil, Speaking out: "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 problem I asked, the leaves of countless trees are added together. , 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 deceiving me. You must be deceiving.
" 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 wrong." "Isn't it wrong? What's wrong with that?" Li He asked slowly
. .
"This..." The devil paused, staring with big eyes and opening and closing his lips for a long time, "There's something wrong... there's something wrong..." "
What's wrong?" Li He asked again.
"Something's wrong..." the devil's voice became smaller.
"What's wrong?"
"That's not right..." 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 are right, this answer is wrong."
"Why?" the devil asked, 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 divergence Series. As we all know, in infinite series, only absolutely convergent series can rearrange the terms without changing the converged values. Therefore, for non-absolutely convergent infinite series S1, the summation order cannot be changed arbitrarily... ..."
"..." The devil listened to Li He's words, and the muscles on his face twitched more and more.
"...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, and asked with a straight face, “The third question, what is it?”
“The third question, It is also related to -1/12. ζ(-1)=-1/12 is a result in the sense of analytic continuation. It has no universal applicability. 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, 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... Calculating the vacuum zero point in quantum field
theory When possible, you will encounter infinite results. In this case, you need to use the ζ function and analytic 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? It exceeds everything in the known material world. In other words, the entire universe combined is not as big as On this value. If this level of energy can be used, even if it is only a handful, the energy contained in it is enough to boil the ocean of the entire world. Li He looked at the devil, his expression became gradually serious, and he said seriously: "The first question I want to
ask The three questions that I really want to ask are: why is the value of vacuum zero-point energy 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 open, and his eyes were blank.
Sweat seeped out from his face, and the muscles on his face were squeezed into a ball.
He stood there as if petrified. , remained motionless and continued in silence.
It was impossible not to be silent, because he... couldn't do this question at all!
"What, you can't answer it?" Li He said, "How about I ask a few more questions?" For example, in the sense of analytical continuation of the Riemann zeta function, how important is ζ(-1)=-1/12 to string theory? The key to verification of grand unified theory? Or the method of extending the quantum decorrelation time..."
"..." As Li He kept talking, the devil couldn't help but raise his head and met Li He's gaze. For a moment, he felt his heart being pinched hard and it became difficult to breathe. . For some reason, he actually wanted to return to the Pampas Box.
He had been waiting in the Pampas Box for a long time and thought about the many possibilities after his release, but he never thought of this kind of possibility. Maybe.
"Why, you can't answer these? "Li He glanced at the devil and continued to ask, "How about you answer something else, such as... quantum superposition state... Schrödinger's cat... quantum tunneling effect..."
Devil: "..." He said this He just wanted to be silent. He didn't want to say anything or 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, After all, I stay here.
So I can only listen to Li He continue to ask: "...What do you think the influence of dark matter on space should be like? ...Where's the dark energy..."
The devil felt extremely manic in his heart, but he didn't dare to be manic at all.
He was scared now, very scared.
But he didn't know what he was afraid of at all.
He only felt that he was not a devil, The young man standing in front of him is.
No, the other person is more terrifying than the devil.
Because the other person keeps 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..." Finally, he collapsed.
He
,
a The devil
clenched his fists and
his eyes were red.
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(End of this chapter)