1900: A physics genius wandering around Europe

Chapter 578: The greatest breakthrough in pure mechanics since Newton! The butterfly effect! The world is chaotic!
In later generations, a concept is often borrowed in some science fiction movies: the butterfly effect.

The description of the butterfly effect is also very poetic:
"A butterfly flapping its wings in South America can cause a tornado in Texas, USA."

The butterfly effect is a chaotic phenomenon.

It shows that there is a variable in the development of any thing.

Especially when the solution of the system is very sensitive to the initial conditions, any slight change can cause huge changes.

In real history, the butterfly effect was proposed by American meteorologist Lorenz (not that Lorenz).

He himself is also known as the "father of chaos theory."

When Lorenz was young, his greatest interest was studying weather changes.

As he grew up, he studied meteorology and mathematics, eventually becoming a professor of meteorology at MIT.

In Lorenz's time, computer technology had matured. Although it was still bulky, at least its usability was greatly improved.

One day in 1961, he used a computer to perform calculations for weather forecasts.

When weather forecasting is transformed into an academic issue, it becomes a very complex dynamic system.

This involves not only fluid mechanics, but also various influencing factors such as magnetic fields.

The more accurate you want your weather forecast to be, the more equations you need to list.

Therefore, computers must be used to solve the problem, as relying on manpower would be too slow.

Unfortunately, the computer performance at that time was far less powerful than that of later generations, and the calculation speed was very slow.

Of course, no matter how slow a computer is, it is still faster than a human.

Lorenz's weather forecast model requires computers to perform calculations in several stages.

For example, first calculate the solution to the first part, then input this solution into the second part, and so on.

All steps are completed by computer.

Before today, Lorenz had already run through the process and calculated a result x.

Not only that, the computer also retains the solution to each part separately.

He mainly wanted to verify it a few more times today.

However, the computer was a little slow, and he didn't want to wait here, so he wanted to go downstairs and have a cup of coffee to relax.

So, he took a break.

How to be lazy?
Logically, he should have the computer start over and begin calculating from the first part.

However, the equations of each part are actually independent, and the first part takes the most time.

So, Lorentz wanted to skip the first part of the calculation.

He thought:
"Anyway, the solution to the first part has already been found."

"Why not just use it as input for the next few parts?"

There really doesn't seem to be anything wrong with this.

It's very much like what graduate students do in order to do less work.

As a professor, Lorentz should have been studying theoretical matters instead of verifying calculation results all day long.

So he went straight to the solution to the first part he had calculated earlier: 0.506.

However, this number is the result of a computer printout and only has three decimal places.

The most accurate result should be to six decimal places: 0.506127.

Lorentz also knew this distinction.

But he was too lazy to waste time operating the computer to find the exact value.

His reasons are also very good.

"Anyway, there is only a one-tenth error, so it won't have much impact on the results."

Just like that, after everything was done, Lorenz went to drink coffee happily.

An hour later, he came back satisfied.

However, when he saw the final calculation results displayed on the computer, he was dumbfounded.

"what?"

"what's the situation?"

"Who changed my data?"

The second calculation result y differs from the first calculation result x by several orders of magnitude.

It can be said to be completely different.

Lorenz found it a little unbelievable.

However, he quickly calmed down and found the key to the problem!

That is the solution to the first part, 0.506.

He knew that the solution was manually input into the computer by himself.

If the computer is calculating by itself, it should use 0.506127 as input.

An error of one ten-thousandth can actually cause such a huge difference in the results.

Lorenz immediately became very interested in this.

He seized this phenomenon and conducted in-depth research.

He used different models to verify this, one of which was the temperature-inhomogeneous fluid model that Ridgway had just proposed.

This model is quite common in the field of meteorology.

Air at higher temperatures tends to rise, while air at lower temperatures tends to fall.

In this model, Lorenz also discovered that input errors can cause drastic changes in results.

In 1963, after two and a half years of systematic research, Lorentz submitted a paper to the National Academy of Sciences.

The title is: "Deterministic Acyclic Flows".

In this paper, he used the word "chaos" for the first time to describe his theory.

As soon as the paper came out, it caused a sensation around the world!

If quantum mechanics denies the determinism of the microscopic world, then chaos theory denies the Laplace-style determinism of the macroscopic world.

This was no less than a bombshell to the scientific community at the time.

The scientific community highly values ​​the importance of chaos theory.

“It has had a profound impact on basic science and has revolutionized humanity’s view of nature since Newton.”

“Chaos theory is the third revolution in physics, and it is as great as relativity and quantum mechanics.”

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Lorenz became instantly famous and ranked among the world's top scientists.

In 1972, in an invited speech, he proposed the famous "butterfly effect" in order to vividly explain chaos theory.

From then on, the butterfly effect has almost become synonymous with chaos theory.

With the rapid development of computers, chaos theory has also continued to develop.

In his later years, Lorenz also proposed the famous "deterministic chaos" theory.

He believes that the human body is a nonlinear chaotic system and that various phenomena in the body are unpredictable.

This unpredictability is the embodiment of vitality.

Today, chaos theory is not only limited to physics, but has also been applied in biology, medicine, and even finance.

Research on it is still ongoing.

At this moment, when Li Qiwei proposed the chaos theory, the shock it caused can be imagined.

The many mechanics masters present only felt their scalps tingling and their souls trembling.

"It's incredible!"

Chaos theory completely overturned their three views.

It was as if a whole new door of truth had been opened for them.

Li Qiwei smiled and said:

"Strictly speaking, chaos theory actually already had a foundation."

"Decades ago, the French mathematician Henri Poincaré proposed the famous three-body problem."

"When he studied a system consisting of three celestial bodies, he found that even if the three-body system was a completely deterministic mechanical system, after a long time, the behavior of the system would become unpredictable."

“This actually includes the concept of chaos.” “It’s just that Poincare didn’t think deeply about this problem from a theoretical perspective.”

Everyone was shocked again!
They were amazed at Professor Bruce's extensive knowledge.

Any knowledge is readily available.

In real history, Poincaré also proposed another famous law: Poincaré's theorem.

That is: in a closed system, any particle will inevitably approach its initial position infinitely after a sufficiently long period of time.

(Note that it can only be infinitely close, there are still slight differences, and it cannot return to the original position.)
Therefore, after a cycle, the system will be infinitely close to the initial state, and such a cycle is called "Poincare recurrence".

Therefore, some people say romantically: I hope to meet you again after a Poincare regression.

Unfortunately, according to chaos theory, after the Poincare regression, the universe will evolve into a completely different space-time due to slight differences in initial conditions.

We can never go back to the past. The "forever" here refers to the "forever" in both mathematical and physical senses.

Just as Li Qiwei was letting his imagination run wild, everyone gradually calmed down.

There was still shock on Plant's face.

However, he raised a question.

"Professor Bruce, is it possible that the chaos phenomenon you mentioned is just a pseudo-random phenomenon caused by the complexity of the calculations?"

“It’s like flipping a coin and calculating whether it lands heads up or tails up.”

"The process appears to be random."

"But as long as we have enough parameters, we can accurately calculate which side is facing up."

Li Qiwei heard this and shook his head slightly.

"That's not the case with chaos theory."

“It doesn’t study the accuracy of a single process, but the series of evolutionary processes of the system.”

"Let me give you a vivid example."

"There was a butterfly on the island of Kalimantan in Asia. It gently flapped its wings, and the disturbance caused by its wings in the atmosphere actually triggered a tsunami in a certain European country."

“This butterfly effect is the essence of chaos theory.”

"Chaos theory is impossible to calculate using mechanical equations."

"Even if we know how much force, angle, and frequency a butterfly uses to flap its wings."

"But the interaction of this disturbance with the surrounding atmosphere is impossible to calculate."

“Even if you can determine the motion of every atom, you can’t be sure which atom will be disturbed.”

“There are countless possibilities.”

"Any deterministic theory, which must be an upper limit to the possibilities, is powerless against this infinite process."

“There is randomness in the evolution of the system itself.”

“Let’s go back to your coin toss example.”

"As long as the equipment is advanced enough, it is indeed possible to calculate with a high probability where the coin will land."

"But if you were to calculate, the coin's fall would indirectly cause an earthquake somewhere in the United States."

“How do you deduce this process?”

"This is what chaos mechanics is really about."

Wow!
Everyone was shocked when they heard this!
The metaphor of the butterfly effect is so vivid and appropriate.

Professor Bruce always uses easy-to-understand language to explain difficult and obscure theories.

Plant couldn't help but nod.

"I understand."

"So chaos theory is a very different way of looking at nature than Newtonian mechanics."

"In Newtonian mechanics, the way the world looks at this moment is determined by the way it looked at the moment before."

“Although we have no way of knowing the process in between.”

"But we believe that it must obey the laws of Newtonian mechanics and has only one state of motion."

"However, according to chaos theory, the process in between is actually unknown."

“Even if we know all the influencing factors, we cannot calculate how the system will evolve.”

"In other words, if time could be turned back."

"Then according to Newtonian mechanics, everything will happen again."

"But according to chaos theory, maybe this moment is not the same as before."

“The world is contingent, not deterministic.”

Wow!
Plant's analysis shocked everyone!
Chaos theory provides people with a new perspective on the changes in nature.

This alone is enough to establish the status of this theory.

Even if it is just a guess now.

But this conjecture gave everyone a direction and confidence to work towards.

Von Karman couldn't help but say:

"Oh, God!"

"This is definitely the greatest breakthrough in the field of pure mechanics since Newton!"

Everyone couldn't help but exclaim!

Professor Bruce gave them a huge surprise.

Mechanics can actually achieve such an epoch-making breakthrough!

Yes, in the eyes of everyone, chaos theory is a groundbreaking theory!
Master Qian Wu was probably the most shocked among everyone present.

He just asked the teacher a question unintentionally, but he didn't expect it would give birth to such a shocking theory.

“Is this also some kind of butterfly effect?”

Then, he couldn't help but raise his own questions.

He said excitedly:

"Professor, is there any difference or connection between the uncertainty in chaos theory and the uncertainty in quantum mechanics?"

After everyone heard this, they all started to think.

This question is also very interesting.

Li Qiwei said:
"Chaos theory is currently just a conjecture I boldly put forward."

"There is still a lot to be learned about this theory."

"But from what I feel right now, I think there is a difference between the two."

“The uncertainty principle in quantum mechanics is a physical mechanism.”

“It has nothing to do with the state of the object or system.”

“Even a particle at rest still has uncertainty.”

"But chaos theory describes the evolving state of a dynamical system."

"For a single atom system, it is impossible for chaos to occur."

“Chaos can only be born if the system is complex enough.”

"And the universe is the largest system known to mankind."

"So, its chaotic effect is the most significant."

"In addition, I think chaos itself is a mechanism of some kind, a mechanism of the macroscopic world."

"We can't explain chaos with underlying principles or rules."

"It is just like the physical concepts such as the speed of light and force. It is an inherent property of the universe as a system."

"It also has some kind of action at a distance."

"For example, if I clap my hands here, maybe it can affect a celestial body outside the observable universe."

"This situation cannot be realized or explained using the existing physics system."

Everyone was shocked when they heard this!
They always feel that chaos theory is shrouded in mystery.

A lively discussion broke out in the room again.

(End of this chapter)