Is our space circle? -- A Discussion on the poicare-based cosmic model

Overview

At the beginning of civilization, human confusion and exploration of time and space have never stopped. The horse is running fast, the fish are diving deep, and the birds are flying high, but the human race is not fast. Why? The reason is that the horse runs fast, but it does not think about why it runs fast. The fish dive deep, but it does not think about why it goes deep; birds fly high, but they don't think about why they fly high, but humans think. When the sun rises from the East and falls from the west every day, I wonder: Does the sun go around the Earth? Confusions make people fantasized about one poetic myth after another. At the same time, the relentless exploration and search for us have made us jump out of the barriers of one thought and headed for the next Olympus. Desire and reality are like the wings of wisdom carrying people's holes in the universe! Starting from the poicare model in the hyperbolic ry, this article presents the author's understanding of time and space through revealing the harbo redshift phenomenon and Galaxy slump (for reference only ).

 

I. poicare Model

The emergence of ry satisfies people's desire to describe the natural world to a great extent. However, with the deep research on ry, more and more mathematicians doubt the rationality of the "fifth Public Design" as a public design. Some mathematicians tried to prove the "fifth Public Design" through the remaining four public settings, but they finally found the equivalent proposition of "fifth public design. At this time, some mathematicians imagine creating another geometric form by modifying the "fifth Public Design". Gaussian was the first person who pointed out that the fifth Public Design of Euclidean was independent of other public ones. He had long known that the attempt to prove this public establishment was in vain. He once told his friends that as early as 1792, he had an idea to establish a logical ry, where the fifth Public Building of Euclidean was not true. There is a kind of ry in the non-European ry that has developed so far called hyperbolic ry, it believes that there are countless lines parallel to known straight lines at a point in the same plane, rather than "one and only one" in the Euclidean ry ". The hyperbolic ry, also known as the robacski ry, has three models in history to explain this ry. The most beautiful and natural model is the poicare model. In the poicare model, poicare considers the disc DR = {(x, y) | X2 + y2 <R2} as the robacski plane, and converts the vertical circumference DR = {(X, y) | the arc or straight line arc of X2 + y2 <R2} is regarded as a non-euro line, the logarithm of the ratio defines the angle between the non-Euclidean distance and the non-European straight line, but is consistent with that in the European ry, as shown in 1.

Figure 1 distance between a non-euro line and a poicare

The non-euro distance between EF and ad is a non-euro line. The non-euro distance between B and C is defined as Ln (B, c; a, d)-1, where (B, c;, d) the ratio between B, C, A and D (B-A) (c-d)/(B-d) (C-). The concept of the poicare metric is obtained based on the fractional linear transformation and the Taylor expansion of the function:

 

Where ds is the poicare distance in the poicare plane, DZ is the corresponding Euclidean distance, r is the radius of the poicare disc, and Z is any point in the dr.

 

Ii. Hubble's Law

The US-based astronomy, Edwin harbo, believes that the forward and backward velocity of the alien series is proportional to the distance, that is, the farther the distance is, the higher the viewing speed.

Here we assume that the center of the Dr center o is the origin of the reference coordinate system and place the reference galaxy at O, and assume that the Euclidean measurement is our actual observation measurement (this is important ). If the theory of the Big Bang is assumed to be true, a certain star system (hereinafter referred to as a "Free Galaxy") starts from the O-point and moves at a uniform speed △vs to the Dr boundary in the poicare metric:

In this case, the X axis in the Delta vs direction coordinate system is:

Then, according to the Hubble law, that is:

(Where)

The monotonicity of functions is: R increases with Z, that is, r = g (z) and is an addition function, that is to say, the expansion degree of the universe is related to the distance from the Free Galaxy to the O point.

 

Iii. Galaxy collapse

In a certain stage of stellar survival, the internal temperature will decrease, so that gravity will become a dominant factor, at this time, the stars began to collapse into "white dwarf stars" and split the atoms into electrons, proton and neutron. In some conditions, gravity overcomes the exclusive force between electrons and forces the electron and proton to combine into neutron, at this time, it is collapsed into a "neutron star". In some conditions, gravity can even overcome the resistance of the neutron structure and continue to collapse.

We know that under the poicare model, we can see that when a graph is moving from the vicinity of the O point to the Dr boundary in a non-European rigid body motion, the European appearance of the image will decrease from the largest to the smallest, the last "disappears from the edge", as shown in figure 2.

 

Figure 2 all the same triangle in the poicare Model

 

Here we make DS the length of the Free Galaxy poicare on the X axis, and DZ the European length of the Free Galaxy on the X axis, then:

 

When the Free Galaxy moves to the Z + Delta Z and Z + 2 Delta Z positions:

Order, there are:

Since the Free Galaxy motion at a constant speed on the poicare metric, it is obvious that the time required for running Z to Z + △z in the poicare metric is shorter than that required to run Z + △z to Z + 2 △z, this shows that the scale-down of the galaxy traveling to the Dr boundary is getting weaker and weaker under the European metric at the time of the poicare metric.

 

Iv. Conjecture

When poicare measures the next non-European Rigid-Body (Free Galaxy) moving at a constant speed to the cosmic border (DR), what will happen when it runs to the Dr border? Obviously, when R is set to Z, what will happen next? There may be two situations:

1. rush out of the limitations of dr. As the galaxy traveling to the Dr boundary is getting weaker and weaker in a European scale, it can be thought that the Free Galaxy has collapsed to the pole before it leaves the dr, after the shackles of DR, it will re-expand into a new universe.

2. The original path is returned. At this time, HC is negative, which means blue shift may occur.

According to the theory of the Big Bang, at the beginning of the formation of the universe, there were different galaxies moving at different speeds along different directions. That is to say, there are Dr with different expansion coefficients in different directions in the space, as shown in 3.

Figure 3 DR with different Expansion Coefficients

According to the second law of thermodynamic, we know that the most possible state is also the most stable, because it is the most disordered, so we have reason to assume that the distribution of galaxy in the universe is in an extremely unordered state. Under this premise, the universe we live in can be considered as an unordered expansion of the opposite sex "sphere ".

 

References:

Stephen Hawking's lecture

Not mysterious non-European ry Li Zhong

Time, space, and everything

Is our space circle? -- A Discussion on the poicare-based cosmic model