science wizard

Chapter 18 Can't do this question!
"Huh? Minus one-twelfth of a leaf." The devil was stunned.

Wei'er and Fei'er, who had been watching from the sidelines, were also stunned after hearing this.

"What... what do you mean?" The devil felt that his brain was a little chaotic, and he couldn't function.

"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 considering your performance in answering the question just now, it's better to explain it clearly.

The first is the score, which is relatively simple. Divide an apple into two evenly, and each apple is half, that is, 1/2. "

While talking, Li Hyuk took out a pocket knife from his pocket, and wrote down the number 1/2 in Fornalenza on the ground.

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 line. 0 is the center point of the number line. To the right means a positive number, to the left means a negative number, and -1 is opposite to 1. -2 and 2 relative to...

For a simpler understanding, you can imagine that you have three apples... Uh, no, you are a devil, and you should prefer souls, so let's use souls as an example.

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

devil:"……"

"Do you understand?" After Li He finished explaining, he looked at the devil and asked.

The devil didn't know why, but there was a feeling in his heart that he didn't want to meet Li He's eyes. He turned sideways slightly, squinted and said with a sullen face, "Of course I understand. How could such a simple thing bother me? Actually... Negative numbers, fractions, what?" Yes, I have it in my memory, but I have been trapped for too long, and my memory is damaged, so I need to remember it slowly."

"Well, that's the best, let's continue and increase the difficulty a little bit." Li He nodded lightly, without questioning the devil, and continued talking.

While talking, 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... the sum of countless leaves, It should be: 1+2+3+4+..., we define it as S.

即S=1+2+3+4+5+6+……；
然后令S1=1-1+1-1+1-1+……；
1-S1=1-1+1-1+1-1+……=S1
So S1=1/2;

再令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；

于是S2=S1/2=1/4；

令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
于是S=（-1/3）S2=-1/12；

既1+2+3+4+5+6+……=-1/12。”

After the derivation, Li He put away the pocket knife, looked at the devil, and said: "The derivation result can actually be simply explained as the Riemann ζ function in the sense of analytic continuation ζ(-1)=-1/12. In short, In my question, 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.

long silence.

The devil stared at the formula written by Li Hyuk on the ground with a pocket knife, and remained motionless and silent for a long time.

After a long time like this, the devil finally spoke out, frowning into a pimple, shaking his head again and again to question: "No, no, your answer is wrong. You are deceiving me.

Yes, you are deceiving me, you must be deceiving me.Countless leaves are added together, and the number will only get bigger and bigger. How can the result become a fraction, and how can it become a negative number?No, this is not right. "

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

"This..." The devil froze, staring wide-eyed, opening and closing his lips for a long time, "It's not right... It's not right..."

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

"It's not right..." The devil's voice became softer.

"What's wrong?"

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

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

"Am I right?" The devil suddenly raised his head and met Li He's gaze, which was a little inconceivable.

"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 a simple example, as I just said, the previous derivation results can simply explain the Riemann ζ function in the sense of analytic continuation ζ (-1)=-1/12, so the = in 1+2+3+4+...=-1/12 cannot be recognized as the = in the conventional sense at all, but refers to 'a function outside the domain of definition The extended value =', there are many attributes...

Another key point, in the process of proving S1=1-1+1-1+...=1/2, there is one thing that cannot be forgotten, S1 is a divergent series.It is well known that among infinite series, only absolutely convergent series can rearrange the terms without changing the converged value.Therefore, for the infinite series S1 that is not absolutely convergent, the order of summation cannot be changed arbitrarily..."

"..." Listening to Li He's words, the devil's facial muscles twitched more and more.

"...From the first step of S1, it is wrong, and the following derivation will naturally be meaningless." Li He finally concluded, and continued after a pause: "Actually, these words are for the second question I want to ask. The answer, but it doesn't matter, we go directly to the third question."

"The third question?" The devil froze for a moment, and asked with a tense 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, and it has no universal applicability. In fact, its application range is very limited. It is generally applied in mathematical number theory, engineering signal processing, physical 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 combines quantum mechanics, special relativity and classical field theory. It is one of the important methods for studying high-energy physics. Many problems in condensed matter physics can be solved by quantum field theory...

In quantum field theory, there is a very important definition called vacuum zero-point energy, that is, the energy contained in the state of vacuum and no 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, so there is energy, and it is because of this that atoms spontaneously radiate. The Lamb shift and the Casimir effect have confirmed this...

When quantum field theory calculates the vacuum zero-point energy, it will encounter infinite results. At this time, it is necessary to use the zeta function and analytic continuation to deal with the divergence problem.After processing, the result obtained is absurdly large, 10^107 joules..."

What is the concept of 10^107 joules?Beyond everything in the known physical world.In other words, the entire universe combined cannot compare to this value.If this level of energy can be used, even if it is just a handful, the energy contained is enough 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 question I really want to ask is, why is the value of the vacuum zero-point energy so large, surpassing the entire world?
What is the principle?Does the magical power contained in the current world play a role in it?Can spell power be explained in quantum field theory?

Mr. Devil, you just said that you have extraordinary intelligence and terrifying power.As an existence with both magical power and excellent intelligence, as a life from the mysterious hell, I think from your point of view, you should have a very good answer for me.Then please give me an explanation-any explanation of these questions is fine. "

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

The expression is stiff, the eyes are wide open, and the gaze is blank.

Sweat seeps from the face, and the muscles on the face are squeezed into a ball.

Like petrification, standing in place, motionless and silent.

It's impossible not to be silent, because he... can't do this question at all!
"Why, you can't answer?" Li He said, "How about I ask a few more questions? For example, in the sense of analytic continuation, the Riemann ζ function ζ(-1)=-1/12 pairs of strings The importance of the theory? The key to the verification of the grand unified theory? Or the method of extending the quantum decorrelation time..."

"..." Li He kept talking, the devil couldn't help but raised his head, and was meeting Li He's gaze. For a moment, he felt his heart being pinched hard, and it was difficult to breathe.For some reason, he actually wanted to go back into the Pampas Box.

He waited for a long time in the Pampas Box, thinking about many possibilities after 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 other questions, such as...quantum superposition state...Schrödinger's cat...quantum tunneling effect... ..."

Devil: "..." He just wanted to be silent at this moment, he didn't want to say anything, and he didn't want to do any thinking.

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

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

So I could only listen to Li He's continued questioning: "...What do you think the influence of dark matter on space should be like?...What about 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.

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

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

No, the other party is more terrifying than the devil.

Because the other party is still talking non-stop.

"...What do you think is the truth of the Big Bang? Or, what do you think is the truth of the birth of the world...Since you have extraordinary intelligence, no matter how incomplete your memory is, you should have some answers to these questions. ..."

Finally, he broke down.

he,
a devil,
clenched fist,
The eyes are red.

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(End of this chapter)