@@@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.
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
Einstein thought that acceleration and gravity are equivalent. The general
theory of relativity (GR) was invented from this equivalence principle
and the special theory of relativity (SR). Einstein used the rigid body
which is not distorted for explanation of distortion of space. The concept
of this rigid body has imagined the substance. If this rigid body runs
by the speed near light on the circumference, acceleration will be produced
and it will produce distortion according to the effect of SR. From this
thought experiment, it was concluded that space was distorted with gravity.
And is is GR which is deduced by doing in this way. The reason for space
being distorted is explained by a substance being distorted. A substance
builds the cause of distortion of space in GR. However, there is no distinction
in space and a substance about distortion produced as a result.
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
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 true inertial system of the universe
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 R, and an object has velocity v against the CMB (the true inertial system). Acceleration of an object
is v2/R. Because, it is for moving along with the curvature of the universe. The
three-dimensional space of the universe is expressed as the spherical surface
in Fig. 1.
Generally, when an object which has inertial mass is accelerated, it tries
to remain in an inertial system. The force is felt to the direction which
remains at an inertial system as a reaction. This idea is applied in the
finite, static, and closed universe.
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=mv2/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 c2/R (R is the curvature radius of the universe).
The force acting on light is below. F=mc2/R. m=E/c2 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=Ι0ex/R@
(Ι: a observed wave length, Ι0 : 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=ex/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.
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 1+z.
Cosmological redshift is z=e2Ξ -1 in 2ΞR light-years away.
Dilation of the time in that place is e2Ξ (about 540) times. And the place is the same place here that went around
the universe. Seemingly this is contradiction. However, it is good to think
that time is dilated to e2Ξ times in 2ΞR years ago.
Generally, time dilation in x years ago is expressed below. T(x)= ex/R @
Time dilation at the x light-year distance is the same time dilation in the universe x years ago.
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.
The simulation of the cosmic microwave background radiation (CMB)
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.
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
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
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
Please allow the mistake in grammar and terms.
Detailed explanation is prepared in Japanese.
Friendly comments are welcomed although I refuse to receive criticism.