In addition to the many touching plots, what excites me most is to see many physical scenes that can only be imagined in the past, which are materialized by Nolan, and so beautiful and magnificent, even if there are many different from the original imagination.
When I saw Ghost at the beginning, I guessed that this was not an ordinary burden. It might be a revelation from future humans, but I didn't expect it to be the male protagonist himself. In the end, the actor entered the five-dimensional space through the black hole, and the plot reached a climax, shaking off all the baggage. There are many concepts of mathematics and physics involved here. I am not a scientist, but just ordinary people who have liked physics for many years. Sheldon and other scientific experts should stop spraying. If there are any problems, you are welcome to communicate more. This article is not correct. Too many comments on the plot are just to help everyone understand the multiple spaces. ,
Before, several concepts first universal
1. [N dimension can be embodied as a N-1 dimensional projection]
a length dimension only, that is a straight line.
Two-dimensional is the length and width, which is a thin slice without thickness (height), so all two-dimensional graphics are projected as a line in one-dimensional. This is not difficult to understand.
Three-dimensional adds height. By analogy, it is the concept of true projection. For example, a three-dimensional sphere is projected into a circle in two dimensions. Note that it is not the measurements.
What about four dimensions? Wait a minute.
2. [In the N+1 dimension, you can connect any two points
in the N dimension by twisting the N dimension] In one dimension, only a straight line between two points is the closest, which becomes a line segment.
On a two-dimensional paper surface, we can also twist this line segment into a circle, then the distance between the two points becomes 0.
In 3D, we can simply distort the paper so that two points touch each other. Just like in the movie. Poke the two holes of the projection with a pen, it is a wormhole, and the three-dimensional projected on the two-dimensional paper is a circle, so it is naturally a spherical in the three-dimensional. I believe it is easy to understand here.
You can understand the distortion in the four dimensions like this: you can go from any place to any place in an instant. We are just distorting the space. More vividly, it is the random door of Doraemon.
For more dimensional distortions, see below.
3. Regarding the collapse of probability waves, [Schrödinger's Cat]
Schrödinger's Cat is a representative one of many quantum puzzles. I believe you have heard the description of this story many times. I will simplify it. "A lively cat is sealed in a secret room. There is a plate of poison in the secret room. I don’t know if the cat will lick the poison. Then you open it. Before the secret room, was the cat alive or dead?"
According to our experience in daily life, it can be determined that the cat is either dead or alive. However, if we use the Schrodinger equation to describe the Schrodinger cat, we can only say that it is in a superposition state of living and inactive. We can only know whether a cat is alive or dead at the moment when we uncover the lid. At this time, the cat's wave function immediately shrinks (or collapses) from the superposition state to a certain state. Quantum theory believes that if we don't open the lid and observe, we will never know whether the cat is dead or alive, and it will always be in a half-dead superposition state.
Is it hard to understand? You just have to imagine like this: the moment you open the lid, the space-time splits become two, one is the cat's death, the other is the cat's alive, these two space-times will continue to exist independently of each other from now on. There are two you in the world, and they may do different things, and these two time and space (universe) will not affect each other. Then before the space fission (that is, the moment you open the secret room), the two space-times are superimposed, and the life and death of the cat is a probability. This probability, or probability wave, turns from the wave to a certain point (the collapse of the probability wave) at the moment you turn it on.
4. [Parallel Universes]
If you understand the possibility of cat's life or death, then you can understand that two parallel universes have been created here. If you add other parameters, for example, if the cat is alive, whether it is standing or sitting; if it is dead, whether it is lying on its stomach or lying down. After adding these four possibilities, there are 4 parallel universes (stand alive, sit alive, lie down, lie down), and so on, there are infinitely many parallel universes.
Next we come to understand the multi-dimensional space.
Four dimensions are three dimensions with time added. If you are also in a four-dimensional space, the person you see should be like this).
http://www.my51a.com/ewebeditor/uploadfile/200998164646650.jpg
http://images.zj.com/uppic/2009/09/04/1276514_2.jpg
should actually be longer than this trajectory, this person’s The whole life is reflected in this long trajectory. Let us call this shape in the picture a "four-dimensional trajectory diagram". And the person we see in the three-dimensional world is just a momentary projection of this long four-dimensional trajectory map. Therefore, the three-dimensionality is a certain moment in the four-dimensionality, and conversely, the four-dimensionality is a collection of three-dimensionality.
The five dimensions are probability (also can be understood as different possibilities), that is, the four dimensions of the parallel universe are added. Then the projection in four dimensions is also a four-dimensional trajectory graph. So what should it look like in a five-dimensional world?
In the five-dimensional, you will see that the same person has countless four-dimensional trajectories (each trajectory is his life, he may become a doctor, he may also become the president, etc.. So in the five-dimensional, There are countless possible lives of this person) superimposed together and projected into any four-dimensional space, the probability wave will collapse into a certain specific state, that is, a certain life of his.
In "Interstellar", after finally entering the black hole, the male protagonist enters the five-dimensional space, which contains all the time periods of his daughter's room. For the convenience of the demonstration, the film does not use the four-dimensional trajectory diagram, but uses countless rooms. . Some people may ask, shouldn't it be four-dimensional? Why is it five-dimensional? Because under the circumstances at the time, his daughter's fate may also be possible, the equation may not be solved, and his information may not be received, etc. Therefore, it is more appropriate to interpret the film as five dimensions.
To add, the two points of four-dimensional distortion and three-dimensionality, which we have discussed above, are random gates. So, how does five dimensions connect two points in four dimensions? We twist any two points (two moments, such as 3 years old and 30 years old) in the four-dimensional trajectory of "someone's life" together, and it seems that this person has suddenly changed from 3 years old to 30 years old. In other words, people in the five-dimensional space can change their time (age) at will.
Let's go one step further, what is six dimensions?
In five dimensions, there are many possibilities in this person's life. You can imagine countless four-dimensional trajectory image toothpicks inserted in the center of a circle, becoming a huge sphere, but each "toothpicks" is independent , There is no direct connection between them. Think of this "toothpick ball" as a projection of six dimensions to five dimensions. If you understand the above [In the N+1 dimension, you can connect any two points in the N dimension by twisting the N dimension], then you can better understand the six dimensions.
In six dimensions, any two points of any two toothpicks of this toothpick ball can be connected at will. Let us take an example. On one of the "toothpicks" (remember, every toothpick is a four-dimensional trajectory diagram, which is a certain kind of this person's life), this person fell down when he was 3 years old and left his face There was a permanent scar; on the other toothpick, this person had no scars at the age of 30. In other words, not only can this person suddenly change from 3 years old to 30 years old, but also suddenly change from 3 years old with scars to 30 years old without scars. In other words, people in the six-dimensional space can not only change their own age, but also change their own destiny, they can experience the life of a scientist, or they can suddenly become a rich man, who can make themselves taller, shorter, and changeable. Thin and strong, you can change whatever life you want to live.
The four-dimensional trajectory diagram of all the infinite possibilities of our existing universe is made into a toothpick ball, which is a five-dimensional world. Then the six-dimensional is a super toothpick ball that can link any two toothpicks.
The six dimensions already contain all the possibilities. Do you dare to imagine the seven dimensions?
Please note that our possibilities are still based on the physical foundation of the current world. For example, a person has a nose and two eyes. The earth also has gravity. The mixture of ice and water is 0 degrees Celsius, and the speed of light is 300,000 kilometers per hour. Seconds...So, are there other universes that are different from the world we live in? If there is, then the two worlds are connected together to form a seven-dimensional.
If the 6th dimension is a super toothpick ball, then the 7th dimension is another super toothpick ball whose physical laws are completely different from the one where we are. Connecting two balls is seven dimensions. In other words, our current universe has become another universe.
Then the eight-dimensional is well understood. Assuming that the universe toothpick ball we are in is A, it can become a toothpick ball B, and it can also become a toothpick ball C. The physical laws of each toothpick ball are different. The eighth dimension is the collection of all the different toothpick balls connected. Think of AB, AC, AD... all the connections as new big toothpicks, and then plug them together to form a "toothpick ball of a toothpick ball", which is eight dimensions. But every big toothpick still doesn't affect each other. We cannot jump from the big toothpick AB to the big toothpick AC.
Nine dimensions can break through the above restrictions and change at will. The universe is already drunk, and you can do whatever you want. You are already a god.
So the ten-dimensional is to gather all of these, and there is no more collection than this.
Let us summarize all the dimensions
: one dimension: length,
two dimensions: width,
three dimensions: height,
four dimensions: time,
five dimensions: probability/possibility,
six dimensions: a collection of all possibilities,
seven dimensions: from our universe to the other
eight dimensions of the universe : A collection of possibilities of different universes.
Nine dimensions: the universe that can be changed at will.
Ten dimensions: everything, everything, everything
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