@@@Japanese @Since October 1, 1997

@@@English @ @ Since January 6, 2008 @@ @Last update March 1, 2008

In Japan, this homepage is most highly supported in the field of cosmology. @@@English @ @ Since January 6, 2008 @@ @Last update March 1, 2008

However, the hypotheses described here have not been accepted in the society of physics and cosmology.

Please read this and judge it by yourself.

**Only the static universe is obtained from the general theory of relativity
**

In SR, the rocket which moves at the speed near light is shortened to a direction of motion. We think that the rocket contracted since the space contracted. People who are in the rocket never think that the rocket and themselves contracted, because a substance and space contract simultaneously. As written previously, GR was invented from SR and the equivalence principle. So, the style of the influence on space must be the same about GR and SR. Only space does not necessarily contract or expand in the idea of GR, and a substance is not left from such change of space. In GR, the idea of the universe to expand is a mistake. And it must be thought that the universe is finite, static, stable, steady state, and closed.

The mistake in the interpretation of GR is the same also in a black hole. Since time stops at the horizon of a phenomenon, a black hole has not been made, as Krauss and its team researcher claim (http://arxiv.org/PS_cache/gr-qc/pdf/0609/0609024v3.pdf ) . We should not consider generation of a black hole from the peculiar time of the falling object, but should consider from an external viewer's time.

If GR is merely used by treating the equation, a fundamental mistake like a black hole will be made. We have to judge in the fundamental idea.

The idea that the universe is finite, static, and closed is not hard to believe. It was the general opinion before 50 years. The average of momenta does not exist in the infinite universe. However, if the universe is finite, the average of the momenta exists there. The existence of the average of the momenta breaks the perfect symmetry of the motion spontaneously. It forms the true inertial system and it must be clearly distinguished from other systems. Such a system is recognized as the cosmic microwave background radiation (CMB), in fact. On the scale of the whole universe, all heavenly bodies are almost being fixed to this system. The innumerable inertial systems which have been considered to be completely equivalent until now is not equivalent. This true inertial system is the special static system, and we can call it the absolute static system. However, this hypothesis does not deny the theory that the speed of light is fixed. The true inertial system or an acceleration system is only distinguished. The frame of the CMB is the true inertial system and others are acceleration systems when it is expressed precisely.

The new view of cosmological redshift

The spherical curvature of the whole universe exists in the finite, static , and closed universe. Suppose the universe has curvature radius

If an object moves against the CMB, it will try to remain at the true inertial
system by the gravity action of the whole universe. That force **F** is the value which multiplied this acceleration by the mass **m** of that object. It is expressed in the following equation.

**F=mv**^{2}/R

And it is the direction which tries to remain at the system which forms the CMB. Apparently this view is the same as the usual Newtonian mechanics. However, the reaction working on a object which moves with the curve of the universe is not the opposite direction of acceleration. It is because the direction of acceleration is a direction which we cannot know.

When this relation is applied also to light, the acceleration of light is**c**^{2}/R (**R** is the curvature radius of the universe).

The force acting on light is below.

**F=mc**^{2}/R.

**m=E/c**^{2} is substituted.

**F=E/R**

(**E** is a energy of photon,@**R** is the curvature radius of the universe)

Light always receives this force from the whole universe as the gravity action. The following equation is obtained from this relation.

**Ι=Ι**_{0}e^{x/R}@

(**Ι**: a observed wave length, **Ι**_{0 }: a emitted wave length,@**e: **base of natural logarithm, **x**: distance to the Galaxy to which light was emitted, **R**: the curvature radius of the universe)

Redshift**z **is expressed below.

**z=e**^{x/R}-1@

This redshift is produced by the gravity action from the whole universe.

Is it accidental? The distance**RH** to the horizon of the universe obtained from the expanding universe which
has fixed expansion speed is the same as the curvature radius **R**.

From the recent data of supernovae ( http://arxiv.org/PS_cache/astro-ph/pdf/0402/0402512v2.pdf ) , the curvature radius of the universe in this static model is about 15 billion light-years. It is shown in Fig. 2.

And it is the direction which tries to remain at the system which forms the CMB. Apparently this view is the same as the usual Newtonian mechanics. However, the reaction working on a object which moves with the curve of the universe is not the opposite direction of acceleration. It is because the direction of acceleration is a direction which we cannot know.

When this relation is applied also to light, the acceleration of light is

The force acting on light is below.

(

Light always receives this force from the whole universe as the gravity action. The following equation is obtained from this relation.

(

Redshift

This redshift is produced by the gravity action from the whole universe.

Is it accidental? The distance

From the recent data of supernovae ( http://arxiv.org/PS_cache/astro-ph/pdf/0402/0402512v2.pdf ) , the curvature radius of the universe in this static model is about 15 billion light-years. It is shown in Fig. 2.

If we are to have in the universe an average density of matter which differs from zero, however small may be that difference, then the universe cannot be quasi-Euclidean. On the contrary, the results of calculation indicate that if matter be distributed uniformly, the universe would necessarily be spherical (or elliptical). Since in reality the detailed distribution of matter is not uniform, the real universe will deviate in individual parts from the spherical, i.e. the universe will be quasi-spherical. But it will be necessarily finite. In fact, the theory supplies us with a simple connection 1 between the space-expanse of the universe and the average density of matter in it.

universe would necessarily be spherical, finite universe.

@Footnotes

1 For the radius R of the universe we obtain the equation

@@@@@@R

The use of the C.G.S. system in this equation gives 2/k = 1.08~10

Einstein says in this literature that in the equation (R

15 billion light-years will be put into R.

R=1.5~10

R

p=1.08~10

According to mainstream ideas (Davidson, Keay & Smoot, George.Wrinkles in Time.New York: Avon, 1993: 158-163) ( http://hypertextbook.com/facts/2000/ChristinaCheng.shtml ) , the universe is probably at critical density. And the density is @3H

It is almost in agreement with the value from the new static model. The value of the density which the mainstream space model predicted has been predicted by the new static model. The advantage of this new model is that unknown parameters such as © and Ά do not exist.

Time dilation and redshift

The cosmological redshift occurs by gravity action from the whole universe, as had already been described.

The image of a distant galaxy is not fuzzy, because in this model, light does not act with substances which exist in the path.

The cause of redshift from distant galaxies and the cause of redshift from heavenly bodies which have strong gravity are gravity, both.

It is thought that progress of time is slow in the far galaxy, because progress of time is slow in the heavenly bodies where gravity is very strong. Both phenomena are the same, and time dilation is in proportion to

Cosmological redshift is

Dilation of the time in that place is

Generally, time dilation in

Time dilation at the

It is said that explanation of a time dilation observed in a type Ia supernova ( http://arxiv.org/PS_cache/astro-ph/pdf/0504/0504481v1.pdf ) is impossible by a tired light theory ( http://www.astro.ucla.edu/~wright/tiredlit.htm ).

However, from my hypothesis, time dilation of the distant supernova can be explained in the static universe.

Recently, it was observed that the CMB is very smooth and very corresponding with blackbody radiation. These observational data are the reason assumed that the big bang cosmology is right.

Nowadays, it is recognized that static cosmology cannot be necessarily denied only in existence of the CMB. Because, there were the people who believe static cosmology, and they predicted the temperature of space precisely and earlier than George Gamow. ( http://redshift.vif.com/JournalFiles/Pre2001/V02NO3PDF/V02N3ASS.PDF )If the reason why the CMB is so corresponding with blackbody radiation and is so smooth can be explained by the static universe model, we must reconsider the big bang theory.

The CMB fluctuations of 1/100,000 in the static universe

If the thermal radiation from particles which exist in outer space is a cause of the CMB, and if temperature fluctuation correlates with the mass density of the space, it is difficult to explain that there is temperature fluctuation of only 1/100,000 in the CMB. Heavenly bodies, such as galaxy, exist in the universe and it is expected that there is more deviation of mass density in space for forming them. From such a reason, it seems that the cosmologist of the mainstream judged immediately that the formation of the CMB by the thermal radiation of outer space is impossible. However, is such a judgment really right? We have to verify this judgement.

The galaxy which exists 10 billion light-years away from us can be seen, and the image of the galaxy and thermal radiation are formed from the same electromagnetic wave. An electromagnetic wave comes even from 10 billion light-year distance. Therefor, about the formation of the CMB by thermal radiation, we have to consider contribution of the thermal radiation not only from the near space but also from the distant space.

We will assume that there is the thermal radiation from the space near our galaxy, and that the temperature fluctuation of the thermal radiation can be simply expressed in a sign curve. When we consider about contribution of the radiation from distant places, many layers of the radiation become like layers of pearl. It is shown in Fig. 3.

We can think that composition of each layer is observed from a center. In the figure drawn on the second dimensions, the number of the waves included in a certain visual angle is proportional to distance.

Three layers near us are considered. The intensity of the radiation which
comes from each layer is the same, as it is in Olbers' paradox. The ratio
of the fluctuations which added three layers is smaller than the ratio
of each layer's fluctuations. Because, it is the average ratio of three
layers. It is shown in Fig. 4 and the equations are below.

**f _{1}(Ζ) = sin(Ζ + Ώ_{1})**

f_{2}(Ζ) = sin(2Ζ + Ώ_{2})

f_{3}(Ζ) = sin(3Ζ + Ώ_{3})

f(Ζ) = osin(Ζ + Ώ_{1}) + sin(2Ζ+ Ώ_{2}) + sin(3Ζ+ Ώ_{3})} / 3

In Fig. 5 the red line shows the ratio of the fluctuations which composed
of 1,000 layers. Compare with the blue sign curve of one layer, the red
line is almost minute oscillation.

Suppose that the fluctuations of the thermal radiation from the space of
less than 1,500,000 light-years near our Galaxy is 1/100. If 1,500,000
light years is made into one layer, 15 billion light-years become 10,000
layers. And if the ratio of the fluctuations from 10,000 layers turns into
about 1/1,000 of one layer, the fluctuations ratio from all layers drops
to 1/100,000 (multiplying 1/100 by 1/1,000). This has not been calculated
exactly. Since, there are dispersion and redshift of the thermal radiation
and Olbers' paradox is not realized correctly. Moreover, both the fluctuations
of one layer and the number of layers have not been examined sufficiently
. Although all are ambiguous, if the thermal radiation from distant space
is taken into consideration, it turns out about that the fluctuations becomes
smooth.

**The CMB is corresponding with blackbody radiation in the static universe**

Conventional cosmologists thought that the thermal radiation from far space
should also come to our place, if background radiation was thermal radiation
from space in the static universe. Since the thermal radiation from distant
space caused redshift, they thought that the curve of a blackbody radiation
could not be maintained. By this idea the CMB is a basis of contradiction
for the static universe.

It is certain that we have to consider how the thermal radiation which
come from distant space is dealt with. However, their conclusion is not
necessarily right. In order to reconsider this problem, I adopt the static
universe model which I advocate, and think that the universe is filled
with 2.725K blackbody radiation of everywhere. If 2.725K blackbody radiation
can be forever maintained in the simulation of this universe model, it
will be a success, but it is a failure if it cannot be maintained.

Although I consider the static universe, it does not consider the frozen
world. There are evolution of celestial objects and dynamic thermal equilibrium,
but it is static as the whole universe. From such a viewpoint, even if
the CMB which fills space is 2.725K blackbody radiation, the substance
to emit does not need to be just 2.725K. The important thing for a dynamic
thermal equilibrium is not that the substance to emit is the same temperature
as radiation of the space. I think that the thermal equilibrium is formed
with some components. That is, if the CMB from distant space receives redshift,
the space substance here should emit the short wavelength whose temperature
is higher than 2.725K, and by it, redshift will be negated and it will
form 2.725K blackbody radiation. Moreover, this is a thing of bidirection.
Distant space's substance is also higher than 2.725K. So, the temperature
of a space substance is higher than 2.725K everywhere. This space substance
compensates the redshifted CMB. And this compensation forms 2.725K blackbody
radiation. In order to form a blackbody radiation, emission of a high temperature
must cover completely the curve of the redshifted CMB.

In order to perform the simulation, the following two equations are used.

(This equation is showing the relation between wavelength Ι and its intensity
B(Ι) in blackbody radiation.)

(This is the equation which already came out in 'The new view of cosmological
redshift'.)

In Fig. 6 the blue curve shows 2.725K blackbody radiation and the each
red curve shows redshifted CMB which come from the distance of 1,500 million
light-years, 4,500 million light-years, and 9 billion light-years. These
peaks of the redshifted CMB are lowered and are shifted to long wavelength.

The red curves have bulged from the blue curve of 2.725K blackbody radiation
in long wavelength. If radiation of a high temperature substance is emitted
to cover these red curves, intensity of the CMB will become larger than
2.725K blackbody radiation. Red curves must be settled inside a blue curve.
For solving this problem, it is a substance which exists in the path from
distant space. While these substance particles emit a thermal radiation,
the electromagnetic waves which come from a distant space will be absorbed.

Various rates of absorption were calculated. On the conditions in which
60% light is absorbed in the distance of 15 billion light-years, the CMB
curves from every distance are almost settled inside the 2.725K blackbody
radiation curve. Even if absorption in 15 billion light-years is beyond
60%, the red curves are settled inside the blackbody radiation. However,
we will think that 60% of light is absorbed in the distance of 15 billion
light-years in this model. It is shown in Fig. 7.

The difference between 2.725K blackbody radiation (blue curve) and the redshifted CMB (red curves) are expressed in green curves. It is shown in Fig. 8. These green curves will be called the compensation curve from now on. And the redshifted CMB should be compensated by the amount of radiation which the compensation curves show.

The CMB does not come to our place suddenly from 9 billion light-year distance.
While moving a slight distance, we should think that the CMB is affected
by this compensation. In Fig. 9 the blackbody radiation of 2.725K is drawn
in blue, and on the condition that 60% of light is absorbed in 15 billion
light-years, the CMB from 150 light-year distance, 1,500 light-year distance,
and 6,000 light-year distance is drawn with the red curves. But, there
is no blue curve and there is only one red curve. The blue curve was drawn
previously, the red curves overlapped and the blue curve has been erased.
Moreover, since there were few differences, three red curves overlapped,
and they became one. Then, in order to know how much those differences
there are, the compensation curves were increased 1 million times with
calculation and expressed as a green line, and they are also shown in Fig.
9. The peak of all compensation curve is 0.818mm in wavelength, And if
magnification is changed and drawn suitably, three compensation curves
will overlap. If the place where the CMB is emitted approaches us infinitely,
it seems that the peak of the compensation curves will be converged on
0.818mm. The blackbody radiation with a 0.818mm peak is the temperature
of 3.59K from the Wien's displacement law (lambdamax=0.002898/T). On the
conditions that 60% of light is absorbed in 15 billion light-years, it
is thought that the redshifted CMB come from distant space is always compensated
by the thermal radiation from the substance of 3.59K, and can maintain
the 2.725K blackbody radiation.

Even if the substance temperature of space is 3.59K, the substance of space
will get cold, because the surrounding background radiation is 2.725K.
However, in order to maintain background radiation of 2.725K, substance
temperature of the space cannot fall. For solving this inconsistency, it
seems that the radiant energy which galaxies etc. release is absorbed by
substance of space. By this absorption, the substance temperature of space
is maintained higher than the temperature of background radiation.

The redshifted CMB is always corrected to 2.725K by the thermal radiation
of the space substance in a slightly high temperature. Thus, 2.725K blackbody
radiation is maintained in the static universe.

If 99.99% of light is absorbed in 15 billion light-years, the temperature
of a space substance will be 2.94K. The temperature of a space substance
approaches 2.725K as an ratio of absorption becomes high. If an ratio of
absorption becomes very high, radiation will almost be absorbed and scattered
in very short distance. It is not necessary to take redshift into consideration,
and is the same as the usual thermal equilibrium.

**The famous astronomer's incomprehensible criticism **

In order to criticize and deny tired light theories, Edward L.Wright the
famous astronomer has described the following statements in his own homepage
( http://www.astro.ucla.edu/~wright/tiredlit.htm ).

In tired light model the CMB must have come from a far away part of the
Universe, and its photons will thus lose energy by the tired light effect.
If the CMB comes from z = 0.1. The CMB starts out as a T = (1+z)*To = 2.998
K blackbody. Because the photons only lose energy but do not decrease their
density, the resulting curve is not a blackbody at To = 2.725, but is instead
(1+z)3 = 1.331 times a blackbody.

( See the link, if you want to know details.)

My opinion is also a kind of tired light theory. Tired light theory does
not explain redshift by expansion of the universe. In tired light theory,
light loses the energy as if got tired while coming from distant galaxies.
It explains cosmological redshift not in the expanding universe but in
the static universe.

Since the static universe satisfies the perfect cosmological principle,
situation of the universe is the same anywhere in tired light model. It
is not the static universe that space temperature is 2.998K in z= 0.1.
Therefore, it is not also the tired light model. He tried to deny tired
light theories. However, he premised the universes other than the static
universe. What on earth does he want to do? I cannot comprehend him at
all.

Please allow the mistake in grammar and terms.

Detailed explanation is prepared in Japanese.

Friendly comments are welcomed although I refuse to receive criticism.

@@by@@Hirokazu Nagata