Site of the Gleaners who think the universe is a spherical surface in at least four-dimensional space


2. Historical second meeting of the Gleaners: A reason why the cosmic microwave background (CMB) is so isotropic


Robot: I hesitate to say this, but G. Snake has passed away just now c in a literal sense.


Puzzle Sheep: If you mean he has died, it's the best news I've ever heard. It teaches us that every arrogant near-sighted man will finally die miserably!


Stamp Pony: I want his bike.


Robot: I said ein a literal sense not spiritual onef. He has just gone away to watch the movie eTransformers: Age of extinctionf, so he won't come back for at least 165 minutes. He asked me to start the meeting.


Puzzle Sheep: Robot, let's take delivery sushi.


Stamp Pony: I want pizza.


Robot: Then I'll order Machine oil Nouveau for me. P. Sheep, why don't you explain our closed universe model and the source or origin of the cosmic microwave background (CMB)?


Puzzle Sheep: We suppose that the universe is the surface S of a sphere as shown in Fig.3. As G. Snake insisted at the first meeting, we only have to consider the paths of rays of light on the surface S in the three-dimensional world. If we spot any point A on the surface S, there is the conjugate point B on the surface S. Rays of light emitted from the conjugate point B converge on the point A.


Stamp Pony: This means that the universe is an absolute instrument.


Puzzle Sheep: Suppose that the earth is at the South Pole of the surface S. Then the conjugate point C of the earth's position is at the North Pole of the surface S. We further suppose that the special theory of relativity holds on the entire surface S. Then it naturally leads to that the sphere is expanding at the speed of light, i.e. the distance between any pair of conjugate points (including the distance between the earth's position and the point C) is expanding at the speed of light. S. Pony, prove this.



Stamp Pony: If two travelers depart from the South Pole in the opposite directions at the speed of light, then if the expansion speed of the universe is less than the speed of light, the two travelers will finally meet at the North Pole and the time paradox will occur. And because the expansion speed cannot exceed the speed of light, the expansion speed is the speed of light. Q. E. D.


Robot: Well done, S. Pony! In other words, the speed of light is determined by the expansion speed of the universe. And our model will hold if the universe is shrinking at the speed of light.


Stamp Pony: When the two travelers meet at the North Pole, the universe will have vanished and the time paradox wonft occur.


Puzzle Sheep: In this model the distance between any pair of conjugate points is 14 billion (more precisely 13.7 billion) light years. 13.7 billion years is the age of the universe. And the distance between the South Pole and the equator is about 7 billion light years.

            In this model the source (or origin) of CMB is the circumference whose center is the North Pole (point C), and the radius r of the source is about one thousandth of the distance between the South and North poles. The radius r is determined by the Z parameter of CMB.

            As shown in Fig. 3, the paths of the rays of CMB are almost the same as the path passing the South and North poles, and the radius r of the source is very short. Thus we can assume that CMB comes from the very small region near the North Pole, and this is the reason why CMB is so isotropic.

            It should be noted that although a path of a ray of light in a four-dimensional space is curved, the path seems to be strait in the three-dimensional world (observable world). And although the source of CMB is a circumference in a four-dimensional space, the source is a spherical surface in the three-dimensional observable world.


Robot: I shall ask you to close the meeting now.


All: We are spherical-surfacelings! We are the Gleaners!


Robot: In Middle English accent!


All: We aren the Gleaners! May our work be not floccinaucinihilipilification!


Robot: You, seemingly or truly stupid surfacelings! Dismissed!


3. Historical third meeting of the Gleaners

(The expansion speed of the universe is probably not accelerated)

A narrow and maybe insecure path to the Gleaners:

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