In 1687, Newton published “The Philosophical Principles of Natural Science”. The view of time and space “evolved” from the place of the sky to a flat and absolutely lost time and space. In Newton’s view of time and space, space is flat without folds!

This straight view of time and space lasted until June 10, 1854, when the great god Riemann published “On the Basic Hypothesis of Geometry” at the University of Göttingen, tearing a deep hole from the flat absolute space. Because time and space will no longer be straight from the beginning, and the low-dimensional and high-dimensional worlds will begin to show hideous features!

Riemannian geometry: the foundation of Einstein’s theory of time and space

General relativity has two basic assumptions, one is the principle of general covariance, or the familiar general principle of relativity; the other is the principle of equivalence.

The principle of equivalence is not difficult to say, but it is a mystery, and it is still a hypothesis up to now! Because it says that the inertial field and the gravitational field are locally indistinguishable, that is, falling at a G-acceleration. In a G-acceleration spacecraft, the inertial force and the gravitational acceleration are equivalent. Even Einstein didn’t know this. Why, but that’s the fact!

The other is the generalized covariance principle, that is, in any coordinate system, the form of the equation remains unchanged. We call it the covariance of the equation, also called symmetry. Its proof requires the mathematical tool of Riemannian geometry, which involves A series of exquisite and beautiful theories to modern differential geometry.

The general theory of relativity collapsed the straight view of space-time and brought scientists into the curved space-time of the modern universe! There is no so-called flat space-time in the universe. Everywhere is curved space-time controlled by mass. Of course, the so-called space-time is related, and time cannot be absolute, and it will indeed collapse the concept of absolute space-time!

From low-dimensional to high-dimensional: what happens if people enter the high-dimensional space-time?

Riemann imagined a two-dimensional creature. The insect crawled on the paper of “One Horse Pingchuan”. It could go back and forth or left and right, but it could not go up and down, but if it was a piece of crumpled paper, then every point the insect crawled over Curvature (Riemann metric) can be described by 6 numbers in a three-dimensional space. Any point in a four-dimensional space needs 20 numbers to describe. The Riemann curvature tensor is just the sum of the number of curvatures described by any point in the space.

It’s a bit dizzy, but it is explained in a familiar way. A certain point in one dimension only needs one length coordinate, while a certain point in two dimensions needs to be described by length and width. Each point in three dimensions needs three coordinates. To describe it, N latitude requires N coordinates to describe it!

Space can only display itself and objects with lower dimensions than it. It cannot display high-dimensional objects. Therefore, all high-dimensional objects displayed in three-dimensional space are schematic diagrams. For example, we can perfectly display two-dimensional and one-dimensional objects on a piece of paper. Zero-dimensional, and the paper itself can be seen as a two-dimensional plane to a certain extent!

It looks like a three-dimensional picture, but it feels flat

So it looks three-dimensional when it is displayed in three dimensions, but it still feels like a flat surface, but that’s okay. We can directly create a three-dimensional object in three dimensions for us to touch, but we can’t create a four-dimensional object anyway. , Because the dimension we are in is three-dimensional.

The Klein bottles in 3D are all fakes

What kind of existence is the four-dimensional space?

Edwin Abbott Abbott described the world in which gods exist in his book “Flat World”. In the two-dimensional world, three-dimensional people have powers that are close to gods, because three-dimensional people only need to stay slightly away from the two-dimensional plane. You can be invisible, and you can observe the world behind the obstacle, and even suddenly appear somewhere on the two-dimensional plane!

Suppose we use analogy, what happens when a person in a four-dimensional space observes a three-dimensional space, is it also for us to have the power of God? He can randomly appear anywhere in the three-dimensional world, and can steal the gold jewelry in the bank vault from an extra dimension that is one more dimension than the three-dimensional. People in the three-dimensional world are unaware of it!

And the distance across light-years in our three-dimensional space, from the perspective of four-dimensional space, it only needs to be directly reached through the extra dimension, and instantaneously across light-years. For a three-dimensional person, isn’t this a god-like existence?

What happens if you enter a four-dimensional space?

As far as understanding is concerned, two-dimensional is a flattened three-dimensional world. Does three-dimensional flatten a four-dimensional world? For the existence of life, three-dimensional is obviously the minimum requirement, because a two-dimensional plane has no thickness and even an atom cannot exist. , So the two-dimensionalization in “Three-Body” is a very terrifying ending!

So in turn, can we three-dimensional people enter the four-dimensional?

First of all, each atom of our body can be calibrated with three coordinates in the three-dimensional space. After entering the four-dimensional space, one coordinate is missing, that is, the body becomes open, and every atom in your body will be completely exposed. In the four-dimensional space, is there a great risk? Any disturbance can be fatal!

So if 4D is an extremely pure space, can we keep our existence?

The physicist Li Miao once wrote a very popular “What will happen when a three-dimensional man enters four-dimensional?” “, the description is very simple, only simple physics knowledge is needed to understand what happens when a three-dimensional human enters four-dimensional!

It may be difficult to form even basic atoms. Why is that? Because the Coulomb force in the four-dimensional space is inversely proportional to the cube of the distance, and because the four-dimensional space uses four coordinates to describe any point, the area of the three-dimensional sphere in the four-dimensional space is proportional to the cube of the distance.

In this way, the orbit between the electron and the nucleus becomes unstable, either falling into the nucleus or flying away from the atom. The nucleus becomes an ion, and the body is most afraid of this effect similar to the electrons being knocked off after ionizing radiation. In this sense, human beings may be ionized after entering the four-dimensional space!

This is still not human, maybe you will doubt life? Therefore, the entry into the four-dimensional space in “Three-Body” does not exist, but the attenuation of the radio signal beyond expectations is a correct inference! The same principle applies to gravity. Gravity is inversely proportional to the square of the distance. Celestial bodies that exist in four-dimensional space are unstable. They may fall apart or collapse into black holes. This is really terrifying!

But we don’t actually need to worry about accidentally breaking in, because scientists have not touched the doorway of the four-dimensional space until now, and they can’t even prove its existence!

Of course, the ideal state is that after real discovering high-dimensional space-time in the future, some kind of field can be used to shield the negative effects of four-dimensional on three-dimensional, but we can reach the universe light-year away in an instant through four-dimensional!

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