The first two days
Xiaobian's circle of friends was simply brushed up by "The Beginning"
Out of curiosity
It took the editor a day to complete the play
Never again dare to look directly into the red plastic bag
"Beginning" mainly tells the story of the protagonists Li Shiqing and Xiao Heyun constantly experiencing cycles on a bus that is about to explode, looking for the truth and stopping the explosion.
But I found that the author did not explain why there was a "loop" in the end. So, I fell into contemplation.
Finally, after thinking about the philosophy of life, I,
Min · G Fat Apostle · Quantum Conqueror · Brush Night Champion · guest
Discover that such a profound physical principle is hidden in the "loop" of this play!
01
Butterflies flapping their wings caused a tornado
There was a bomb on the bus, and the bomb was expected to detonate on the bridge at 1:45. And you, the chosen one, gained the power to read the file and keep the memory.
Please use your abilities to find the killer, stop the explosion, and save the passengers.
The protagonists of "Beginnings" have such magical powers that they try their best to stop the bomb from exploding. However, compared with the planned bell explosion, accidentally hitting the tanker truck, manual detonation bombs accounted for the majority.
The female protagonist interferes with the driver's driving, which may cause the bus to crash into the tanker truck; directly call the police, which may be considered by the police to be the perpetrator of the explosion; subdue Tao Yinghong by force, and compete for the pressure cooker may cause the bomb to detonate in advance...
In general, each cycle leads to a different ending due to the different actions of the protagonists.
I will do this!
Isn't this a non-linear chaotic system?
“
Linearity is always boring,
The non-linear world is colorful.
- Minkhailovsky
(I made it myself)
”
First, let's look at a simple mathematical recursive relationship
where r > 0 is a pre-set parameter.
For example, when r = 2, x = 0.9, this number is listed
When r = 2, x = 0.3, this number is listed
We found that at this time, no matter what the initial value is taken, the sequence will eventually converge to 0.5.
Let's then increase the argument so that r = 2.5, the initial x is still equal to 0.9. At this point the calculated number is listed
As you can see, the sequence will still stabilize to a definite value, but at this time more times need to be calculated.
However, if you continue to increase the parameters, when r increases above 3 and below 3.4, the final pattern will be the alternating appearance of two numbers, and when r continues to increase, the sequence will gradually become a four-digit loop, then eight numbers, sixteen digits...
When the parameter continues to increase to 3.57, the period is so long that no matter how long a person is, it is impossible to find a law, or the periodicity has disappeared and entered chaos.
The relationship between the fixed points of the sequence (vertical axis) and the parameters (horizontal axis).
Let's take it a step further and look at a slightly more complex example. In 1963, meteorologist Edward M. Lorentz proposed a simplified model of atmospheric convection,
Since then, people's research on chaotic systems has been pushed to a climax. He explained in 1963 that "if this theory is correct, a seagull flapping its wings could change the weather forever.".
He later used a more poetic explanation, "A butterfly in the Amazon basin of South America flapping its wings would likely cause a tornado in Texas in the United States in two weeks." Thus, chaos is again figuratively known as the "butterfly effect".
A solution to Lorentz's equation that describes the evolution of system states | Image source: Lorenz system - Wikipedia
You can see that the state of the system seems to be spinning around in two circles all the time. In the example of the sequence above, when the argument r = 2, the last sequence converges to 0.5 regardless of the initial value. As such, a system has a tendency to develop toward a certain steady state, and this steady state is called an attractor.
Attractors are a set of states that a system tends to tend to evolve in a variety of starting conditions. The attractor can be a point, a set of points, a curve, or even a complex set with a fractal structure.
At the same time, lorentz's equations are very sensitive to initial conditions, so in practice, even without quantum effects, our predictions of the future could fail because of small differences in the initial values.
With respect to the Lorentz equation for the y variable, the initial value of x, z is conditionally unchanged. The initial conditions for changing only y are 1.001, 1.0001 and 1.00001, respectively. Over time, the differences are getting bigger and bigger | Image credit: Chaos theory - Wikipedia
Nonlinear and chaotic theory is now widely used in various fields, mathematics, physics, biology, and even psychology in non-natural science fields, economics can see his shadow.
In economics, for example, chaos theory can be applied through recurrence quantification analysis (RQA). GIUSEPPE ORLANDO and GIOVANNA ZIMATORE used U.S. GDP data retrieved from the OECD database for recursive quantitative analysis. They examined the correlation of RQA on simple signals and then investigated its application in commercial time series.
02
Iterate through all possible
As everyone knows
Undecided
quantum mechanics
When I saw that the protagonists could cycle through and over again to try various ways to stop the bomb from exploding, I knew that they might have mastered the mysteries of quantum mechanics.
Don't worry, let me sell it.
Quantum mechanics tells us that matter has both wave properties and particle properties, which is "wave-particle duality." So just as water waves stir up patterns as they pass through obstacles, photons and electrons diffraction occur when they pass through slits.
Electron double-slit interference result graph, eventually there will be a significant diffraction pattern
To explain this phenomenon, we need to abandon the traditional idea of "path" and replace it with the idea of "probability.".
In quantum mechanics , the probability amplitude is the complex number that describes the behavior of the system , and the modulus of this complex number represents the probability density. A complex number in the complex plane is equivalent to a vector.
Consider an electron diffraction experiment that emits electrons from point S and receives electrons at point O, passing through a barrier in the middle and having two slits on the screen A, A. The probability amplitude of the electron at O point is the superposition of the probability amplitude of the two paths from A and A.
At this time, a curious student asked, if this is a barrier with three slits (A, A, A), what would the electronic probability amplitude of the O point look like? Obviously it is a superposition of three paths A, A, A.
If he went on to ask, what would the electron odds of the O-spot look like if another barrier with a slit was placed?
This seems like a very stupid question, isn't it just superimposing all the paths? But in fact, you can start from this concept, constantly increasing the screen, increasing the slits, until there are infinite, so that you can get feynman path integrals.
I know people don't like to look at formulas (and I don't either), so here's a picture to illustrate the calculation of the Feynman path integrals of free particles.
There are many possible paths for particles to propagate from point A to point B, and each possible path will contribute to the probability amplitude of point B, and the weight of its contribution is expressed as
where S is the amount of action and is the reduced Planck constant.
The contribution of a set of paths to the integral of free particle paths | Path integral formulation - Wikipedia
We need to add up the amplitude of probabilities obtained by each path and reflect it in the complex plane, that is, to connect each small vector arrow end to end, and the final total vector is the connection from the very beginning point to the last point. The modulus of the probability amplitude is the probability of the emergence of the B-point particle.
Note that the vector AB in the figure above represents the magnitude of the probability of a particle propagating from A to B, and its modulus represents the probability. The area boxed in the figure below represents a small area that has not been offset after the path integration, and when the classical approximation of zero is taken, it transitions to the classical case of propagation along a straight line
In the process of summation, those very outrageous paths cancel each other out in the summation process, the probability is extremely small; only the path in a small area will not cancel, when the reduced Planck's constant tends to zero, the quanta will transition to the classical case, which is what we know as "light propagating in a straight line".
03
Back to the beginning
After such a big circle, let's reveal the secret of the cycle!
The male and female protagonists in "Beginnings" must be familiar with nonlinear physics, because they clearly know that their actions will trigger a series of reactions that lead to completely different results; at the same time, they also have a solid foundation in quantum mechanics, understanding that path integration is to sum all possible paths. So they go through the loops, sort out their ideas, and finally stop the explosion to save everyone, just like the particles finally find the "way" to the end.
Therefore, this wave is a big victory in quantum mechanics!
Finally, in order to alleviate everyone's fatigue after reading the article, Xiaobian specially selected a piece of soothing music at the end of the article, you may wish to close your eyes and listen for a while to relax your mood
bibliography
[1] Lorenz system - Wikipedia
[2] Chaos theory - Wikipedia
[3] Orlando G , Zimatore G . RQA correlations on real business cycles time series[J]. Social ence Electronic Publishing, 2017.
Hao Bolin. From Parabola (Introduction to Chaotic Dynamics) (2nd Edition)[M]. Peking University Press.
[5] Path integral formulation - Wikipedia
[6] Zee, Anthony. Quantum field theory in a nutshell. Vol. 7. Princeton university press, 2010.
Edited by: Min Ke