Site of the Gleaners who think the universe is a spherical surface
in at least four-dimensional space
3. Historical third meeting of the Gleaners: A reason why the
expansion speed of the universe seems to be accelerated
Robot: The subject
of this meeting is to discuss the reason why the expansion speed of the universe
seems to be accelerated. And in my knowledge the acceleration of the expansion speed
is supposed to have started about 7 billion years after the Big Bang.
Puzzle Sheep: As we showed in the second meeting, if we assume that the special theory
of relativity holds on the entire closed universe, the expansion speed
of the universe will be automatically the speed of light. However, some
phenomena looking like acceleration of the expansion speed have been observed,
so we have to explain it in terms of the closed universe.
G. Snake, since you were absent from the second meeting, it's your turn
to explain it.
Glass Snake: I was almost killed by you, but I'm alive here. First I will show you
an optical property of the closed universe using Fig. 4 that is a three-dimensional
representation of the closed universe. The universe is the surface S of
a sphere and the earth is supposed to be at the South Pole on the surface
S.
Then suppose that objects A1 and A3 exist on the equator and other objects
A2 and A4 exist on the areas between the equator and the North Pole and
the South Pole and the equator, respectively. The objects A1-A4 have the
same radius b. The rays of light that determine the angular aperture a1
of the object A1 will take the parts of the paths passing the South and
North Poles, while the rays of light that determine the angular aperture
a2 of the objects A2 will take the parts of the wider paths passing the
South and North Poles. Thus the angular aperture a2 of the object A2 is
wider than the angular aperture a1 of the object A1. If the object A2 goes
nearer and nearer to the North Pole, the angular aperture a2 will become
wider. This is one of the strange optical properties of the closed universe.
Stamp Pony: The
extreme case is the cosmic microwave background (CMB).
Because the source of CMB is almost on the point C (the North Pole) as discussed in the second meeting,
CMB is spread all over the sky on the earth, and the amount of the detected CMB in all directions is almost the same
as the amount of the emitted light from the source of CMB.
Glass Snake: On
the other hand, as is the case in an open universe model, the angular aperture of
the object A4 is wider than the angular aperture of the object A3.
Because of the optical property of the closed universe, if a supernova
has been discovered in the area between the equator and the North Pole
like the object A2, the supernova will be observed bigger and brighter
than the expected size and brightness. Since the distance between the South
Pole and the equator is about 7 billion light years, the birth day of the
supernova is within 7 billion years from the Big Bang. This means that
the brightness of supernovas seems to have changed at the time 7 billion
years after the Big Bang.
Puzzle Sheep: The
phenomenon was interpreted as the acceleration of the expansion speed started
about 7 billion years after the Big Bang in an open universe model.
Thus our closed universe model doesn't contradict the observation.
Robot: I shall
ask you to close the meeting now.
All: We are
spherical-surfacelings! We are the Gleaners!
Robot: In Klingon accent! (Klingon grammar is described in WIKIPEDIA)
All: Gleaners' maH! Qapla'!
Robot: In Esperanto accent!
All: Ni estas la Gleaners!
Robot: You, scaramouch surfacelings! Dismissed!
4. Historical fourth meeting of the Gleaners
(A direct method of confirming that the universe is closed, but …)
A narrow and maybe insecure path to the Gleaners:
(Mail
to: o-pat-consulting@hotmail.co.jp)