Ryndyuk Konstantin Dmitrievich

The study of early unknown properties of space-time

and their influence on Universe modeling

Naryan-Mar, 2014

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The aim of the writing of this work is an attempt to provide a fresh view of evolution of the Universe, which appeared in the course of studying (we with great care will call them so) previously unexplored properties of space-time. The conclusions, that have been received after considering this "new" space-time properties, questioned the correctness of the prevailing currently in the scientific community concepts about the expanding Universe, about the Big Bang, about the Dark Mass and about the Dark Energy.

Let briefly to explain up the essence of these concepts, which we are going to criticize:

This theory assumes in its basis that in the beginning (or before the beginning, as you prefer) the matter in the Universe was concentrated inside the negligibly small volume with indefinitely great temperature and pressure. Then, according to the script, this substance was exploded up with monstrous force. This explosion produced a huge lot of superheated ionized gas, or plasma. The plasma has been expanding homogeneously until it was cooled down up to such a degree that it was been turned into an ordinary gas. Many galaxies appeared inside of this cooled cloud of expanding gas, and inside of these galaxies, generations of the stars were born there. Then, a lot of planets as our Earth, appeared around of these stars. [1]

The main

1. Creation of a mental construction

1.1 An agreement about the terms

Although concepts such as expanding Universe and the Big Bang are being disproved by the conclusions of this research, we shall continue to use terminology from these hypotheses, by virtue of established traditions of the scientific community. We will particularly apply such terms as the radial velocity, removing, the rate of the removal, but also we will be to express of the value of the red shift in kilometers per second.

Now we will explain the essence of this work:

We found out that the space-time possesses some unique properties, which are very similar to the properties of the complex space, nevertheless the author does not dare to assert it definitely, that this the same a complex space. As for the properties of a space-time, about which described in its article, although properly speaking, they are not properties of "the complex space", we also will apply some terms referring to concept of a complex space due to their accuracy and expressiveness. As examples may be use such terms are as "the real one's" and as "the imaginary one's", also the term "complex" is in meaning as composite or compound.

1.2 A mental construction

We found out that the Observed distance of space consists out of the vector sum of Real and Imaginary components. Not to frighten unsophisticated readers by using such "an odd and terrible" term as complex space, let us explain the reasons of dividing the space into Real and Imaginary parts. This division is made in order to avoid confusion between the Observed distances and Real distances, which are placed between the Objects and the Observer. By the way, owning to this confusion, one had brought forth an illusion about that there is deficit of substance available in the Universe, which, in its turn, brought forth a hypothesis about the presence of the Dark matter; this issue will be discussed below.

For an ease of the explanation we will offer the following mental construction. For what is it we need? Its aim is to try to pull out our beliefs on surface of a sanity out of sticky morass of images being inspired by the Standard Theory. We need to find such a solid basis to make a separation the Real from the Virtual, also the Actual from the Mythical. How are we to reconcile the irreconcilable points of view? The thoughtful reader can read it all, at the end of this book in an appendix "Some conclusions". Therefore, in our mental construction we have the Real one's and the Imaginary one's which are presented here, but all it in a structured way.

In theory, any such "the Real one's" and "the Imaginary one's" components may be considered, but in practice, we deal only with their complex resultant the Observed distance. Taking the forestalling of this question, we shall note that these properties of an illusory space-time doing its effect only on a large intergalactic distances, which gave an impulse for revising the views about evolution of the Universe.

Above we mentioned a term of the vector sum. The vector sum, according to the Pythagorean Theorem, means that the hypotenuse length of a right triangle which is equal to square root out of sum of square sides. Let us show it on the Picture 1

Picture 1

Picture 1

(hypotenuse length (AC) is always larger than side length of a triangle (AB). This property of hypotenuse will be required us during our further explanation).

Above we have mentioned about «the complex space». If we were speaking about the true complex space, then we would take a root of difference of squares instead of a sum, by virtue of the properties of the complex space.

Now we shall imagine, that the segment (AB) which is laid on the horizontal line and presents itself a real component of distance, and perpendicular to it, i. e. vertically, lies the segment (BC) - it is an imaginary component of distance. On this scheme, we see the Observed distance (AC) this is a hypotenuse of the right-angled triangle, which will be equal to the vector sum of triangle sides (AB) and (BC), as shown below.

Note that the points A, B, C are laying in the same plane, that is through these three points can be spend a plane. And as we have previously agreed that it will be a complex plane, then the Real direction (previously we have agreed to consider this is to be on a horizontal direction) and the Imaginary (perpendicular to the horizontal, that is, the vertical direction).

Let's will put the Observer at the point O of this complex plane. So that he will to observe for the Object M located in point P, (this object can be a Star, a Galaxy, a Quasar, etc.) which is placed at real distance R = (OP) from the Observer.

Above there were some cautious hints about ‘an early-unknown properties’ of the space-time. What do we know about them? (Some factors influencing on these properties of the space-time are given in Appendix #1.)

1.3 The physical meaning of the "new" properties of space-time

The physical meaning of this new property of the space-time is that "...due to the fact that all Objects in the Universe emit the energy, around of these objects the property of the space-time is changed. The change of the property is manifested as an increase in the time delay of the signal between the Object and the Observer. In addition, that an increase of the travel time of the signal from the Object is equivalent to the fact that this Object is observed farther. The shift of the spectrum of radiation in the red side (i.e. the effect of the red shift) also shows that the travel time of the signal is increased. Continuous influence of this factor leads to the fact that the Object is observed farther and farther, so that is seem to us, it is removed from the Observer..."

1.4 Amendments to the mental construction

Let's back to our scheme. On this complex plane we have an Observer at the point O, Which who is watching the Object M, which located at the point P, (an Object can be a Star, Galaxy, Quasar etc), located it on the Real distance R = (OP) from the Observer.

Let's will add to it the followings: from out the point P, in the upwards direction, the perpendicular to the horizontal direction, shall mark a segment PP*. The point P* and the segment itself PP*, also lie on the imaginary direction.

Let's focus our attention on the fact that the Object does not move from Observer. However, we observe this Object how if it moving away from us. So that, if to consider it all on the complex plane, the Object M from point P "moved" to in the imaginary direction (that is, the perpendicular to the Real direction, i.e. vertically) up to the point P*.

Here, we see that the Object M has made the Imaginary displacement.

So that the Observed distance S from the Object to the Observer, which located at the point O is already a geometrical sum (a vector sum) of the Real distance

and the Imaginary displacement

It's a starting position of the system "Object - Observer".

Let's us will draw the arc with the centre in the point and radius of its equal to S = (*) up to the Horizontal line upon which the segment () is laying itself, so shall found the position of the point 1 .

Picture 2

The next position of the system after a long of time.

The observer "sees" how the Object M has "moved" from the point P along an beam to the point P1. Right now we see that this Object M is observed further from the Observer, on the distance S.

Once again, let us focus on the fact that this Object has remained on Real distance R from the Observer, but has been observed "farther" - on the distance S. In relation to the Object M, we have two distances: the Real distance R and Observed distance S, as well as we have the Imaginary displacement it is the distance of the imaginary moving.

1.5 An important note

As mentioned above, in the course of the theoretical abstraction we can show that the Object has "moving" away from the Observer along the beam; as a rule, in practice we cannot do it. Not possible see plainly this process how the Object is moving away from the Observer, even if this observation is carried out for many centuries. It is impossible to see from Earth the moving of the Galaxies even with the most powerful telescopes. We can only see motionless pictures. We can fix that red shift of the Object spectrum has increased. An increasing of the red shift, as well as the red shift effect in the context of hypothesis of the Universe expansion may be explained as the Object's receding from the Observer.

2. Properties of the space-time

2.1 Factors affecting red shift

Now let's pay attention at the "new" property of the space-time, which one we are aiming to investigate. Let's more fully describe all the factors, from which its property depend on.

We shall start from mentioning that the red shift in radiation spectrum may be caused by the following reasons:

☀  a receding source of the radiation from the Observer, i.e. it's a manifestation of the Doppler's principle;

☀  a movement of light through the gravitational field, with partial loss of the energy and in consequence of occurring of the red shift (Appendix #2);

☀  it's may be some early-unknown space-time properties, which one may become the cause of effect of the the red shift , which one as we learn further depends on emission power, to put it more precisely from a relative emission power.

2.2 Lagrange function

The following statement was presented above - "...Because all objects in the Universe are radiated the energy around themselves, that so the properties of the space-time around these objects are being changed..."

Let's have a detailed look at the system consisting of the Physical body (the Object) which is radiating energy around itself, and the space surrounding of this body. So as the Body is radiating energy around itself, so the whole energy of this system obviously depends on time. Therefore, partial derivative by time should be added into the Lagrange function, which determines the movement of the system,

(the conclusion of the formula in Appendix #3). As a result, we have the following:

If the system is not depended on time obviously, then its partial derivative by time should be an equal to zero,

so that the Lagrange function defining the system condition should have more simpler view:

Let us take this formula and shall compare with the foregoing formula. Here is the following designations in these formulas:

- is an acceleration of the particle (the second derivative of the coordinate change by time) in this area of the space;

- here a generalized velocity of the motion of the particle, where the indexes i, j, k are accepting the values as: i, j, k = 1, 2, 3;

- here is a particle acceleration under the influence of stationary curved space-time, which exists around the Accumulation of the Mass of Matter;


- is here a connectedness (the Christoffel's symbols) which determines the curve of the space-time under the influence of the Accumulation of the Mass of Matter;

- is an additional particle acceleration under the influence of energy change factor in this volume of the space-time;


- is a connectedness which determines the curve of the space-time under the influence of energy change factor in this volume of the space-time.

The analysis and comparison of these formulas shows qualitatively us that if the body began to radiate energy, simultaneously with it, an environment (the space-time) which surrounds this body changes its properties around this body - as it shows an additional connectedness. (Here has been given "qualitatively" estimation, but obviously is not possible to do any practical calculations with these formulas).

2.3 The concept of relative emission power

Right now we shall to clarify the formulation of "new" property of the space-time, about which was previously mentioned:

"...If the body radiates the energy, i.e. the process of the energy liberation is taking place here. Thus, the more intensive process of liberation of the energy (or absorption) in this point of an area is, the more significant of change of properties of the space-time will be occurring especially in this point of an area of space. That is all the changes of properties of the space-time directly depend on the relative emission power of the energy in this point of the area of space..."

Let's specify, that "the relative emission power" (we shall designate it as H) we name a ratio. In numerator we have the value of the process of liberation of energy i.e. power (marked as N) in this area of the space. In other hand, in denominator we have the value of the all-total available energy (marked as E) which is being existing in same area (of the volume) of space.

Where is:

N - wattage of the process of the liberation of energy (an energy emission),

- is energy (in Joule) of this area (of volume) of space,

- is dimension of the relative emission power.

2.4 The single rectangular parallelepiped

It was obtained, that the properties change of the space-time show themselves as downsizing the volume of this body, in other words its compression. It is so because the parallelepiped volume change, made up on the basis of a determinant of the metric tensor of the space-time, also in direct ratio depends on the relative emission power of energy which flowing in this space area. (Appendix #4)

Or in plain words: "...If the body radiates energy, the space-time around this body is changing, so that this area of space shrinks (decreases in volume), and then shrinks and the body itself, which occupies this space..." This functional dependence is expressed by formula:



where - is expresses the properties change of the space-time, it is a change of a unit volume of the parallelepiped which made up on a basis of a metric tensor. The minus sign "-" shows us that the volume decreases as it shown in this expression. And together with the decreasing of the volume, would be decreased the linear dimensions of this body (its length) too.

2.5 The interval

Thus, it is necessary to pay special attention: General Relativity (GR) is formed on a principle of "the conservation of constancy of interval".

If the spatial component of the interval is changed, then the temporal component of the interval does not remain without changes too.


- is the temporal component of the interval.

It is all in plain words: "...the volume decreases, while time interval increases". The delay of a time of the signal from the Object up to the Observer is increasing. This increase of the signal delay is manifesting itself as an effect of the red shift. A.L. Zelmanov pointed at this phenomenon in his work: [2] A.L. Zelmanov "Chronometric invariants and accompanying coordinates in General Relativity" Reports of the Academy of sciences of the USSR, 1956, vol. 107, # 6, p. 815. (Appendix #5)

literally - "...this non-relativistic effect is similar to the Doppler effect caused by the reference system deformation...".

3. Red shift

3.1 A formula of the red shift

In general, that turns out such long "chain" of the cause-and-effect relations:
"...That if any object radiates the energy,
- Its properties of the space-time are changing around of this object;
- The changing of the properties of the space-time is manifested itself as an increase of time of delay of the signal from the Object up to the Observer in particular;
- The Observer will record an increase of time of delay of the signal as the manifestation of effect of the red shift at the spectrum of the Object which its is radiating..."

Naturally, the question arises: is it possible it would be in short. Yes, such a formula was discovered. (Appendix #6) This formula showed us the influence of the object radiation on its object's red shift in the spectrum of radiation.

Here is:

Where is:

-the Distance from the Object up to the Observer,

c - is velocity of light in vacuum,

- is the relative emission power,

- is cyclic frequency,

- is the red shift; the red shift which shall be defined on wave-length (the frequency of wave).

In this formula shown, that the red shift effect - is directly proportional to the relative emission power , as well as, that this value to a first approximation proportional to distance from the Object up to the Observer.

There are an intuitive guesses about an existence of the dependence between the Red Shift from Relative Emission Power by the A.A. Grishaev's article [3]

3.2 A comparison of the Formulas of Red Shift and the Hubble Law

Let's make in this formula some the "cunning" transformations.

Let us express:

through : , and

we shall write as , that is

, and

we shall write through z.

For one's turn, we are known that

- is the "Radial velocity" of the object (in the expanding Universe concept).

As a result, we shall receive the following:

Then we will continue the transformation: we will replace the expression

upon The both parts of the expression we will multiply upon the r, so we will receive the expression

Next will swap both parts - we will finally receive the expression:

This formula shows us, that - the "radial velocity" of the Object , which has been measured by means of the red shift, is directly proportional to the distance r up to the Object. As well as is directly proportional to the relative emission power of this Object.

Now let's compare it (this formula) to the Hubble law, which shows us, that - "the radial velocity of the Galaxy (of the Object) measured by means of the red shift is proportional to the distance r up to it" - that is


These both formulas are very similar, ain't you? As it will be shown below - the Hubble constant (parameter) is the mean value of the relative emission power of all Objects in the Universe. In other words, it represents itself the mean value of the relative emission power of the Universe as a whole. In this fact lies the difficulty of accurate calculations.

3.3 The supplemental information

However, there are many various values of the Hubble constant, which were received by scientists in the various years. In 1929 year had obtained the value of Hubble constant which was equal to 500. In 1931 year it was equal to 550. In 1936 year it was equal to 520 or to 526. In 1950 year it had been obtained as 260, then it has considerably fallen. In 1956 year, it has fallen up to 176 or 180. In 1958 year it has fallen, still more downwards, up to 75, but in 1968 it has jumped back up to 98. In 1972, by the highest standards, it reached from up 50 to 130. Today, the Hubble constant value has been accepted as 55. Nevertheless, the different observers receive the various Hubble constant values yet. Tammann and Sandage are giving 55 plus or a minus 5. Abell and Eastmond are finding it to 47 plus or a minus 5. Then Van den Bergh has calculated between 93 and 111. As an illustration, Heidmann has given the Hubble constant value as 100. De Vaucoulers has come to 100 plus or a minus 10. (The Hubble constant is counted in kilometers per second on megaparsec).

4. Properties of space-time - continuation

4.1 A manifestation of the "new" properties of space-time

All these manifestation of "new" space-time properties have been defined on the base of above-mentioned statements:

- A miniaturizing of a visible transverse dimension of the body d;



- An increasing of the time delay of signal which is coming from Object up to the Observer;

Let sum it up and give an answer on the previously specified question:

-"How is manifested a "new" property of the space-time?"

-"What are the factors from which it depends on"?

☀ This property of the space-time is beginning to manifest its influence when the flow of the energy is been acting in any spatial region. That is, when the Body (the Object) starts to radiate or (to absorb) the energy around itself;

☀ The exterior Observer "is seeing" (if he will observe an inordinate length of time, an endless amount of millions years) that a Body (an Object) starts to be compressed, that is it decreases in volume, as well as the visible transverse dimension of the body d decreases too;

Accordingly, we shall result some formulas define for the transverse dimension of the body d:


(The body lateral dimensions are practically not observed in Astronomy, so they are calculated using the indirect method, so that a check-up of the aforecited formulas are becoming very complicated.)

☀  Being observed also an increase of the time delay of the signal from this Object up to the Observer;

☀  Red shift appeared in the spectrum of radiation of the Object.

Comparing with two last observations is as - "an increase the time delay of the signal" and "an increase an effect of the red shift" the observer is drew a conclusion that this Object "moving" away from him.

An above-named property of the space-time is directly proportional depended on the relative emission power of the flow of the energy, which is taking place in this spatial region. That is, it depends on the relative emission power of the Object H and also depends on from the time of action of the factor . As is easy to see, that all these changes (i.e. an increase signal time delay) "is operating" with a progressive total, being accumulated and summed up.

Let us clarify our computations.

We have done the following operation with the aforecited formula

we are replaced the variable r instead the expression

After all, we have received

Our next operation will be reduction on c,

We swapped the place of the value of to the left-hand side of this equation from the right-hand part, as a result, we received the following:

or .

Let have a look more attentively at last expression

Evidently the red shift z is the result from the product of two variables:

H - which may change itself on a large scale (a cycle is consisting from birth of the star and death of its)

and a variable

- which grows permanently.

We think it will be faithfully to present this formula as the sum:

and passing from summation to integration, then possible to write the following:

However, this change of the properties of the space-time is so insignificant in itself, so they becoming visible only after the expiration of long time (Millions and Billions years).

For example, the data of our Sun

By the way, by this (ability for accumulation and summation) can to explain for such phenomenon as "acceleration of the Universe expansion".

4.2 Two dimensions of time

How to compute these changes using for it aforecited formulas - such as:

Let's find the ratio for two velocities. It is the formula which is connecting the changing of the interval of time from the rate of movement

in the Special Relativity (SR), where the factor - is the ratio of the rate of movement to the c velocity of light. We will substitute the instead of the . Now we will receive the following formula:

having replaced the values of instead of the . In case, is to substitute the expression taking the , then we shall receive a certain remarkable formula,

which is to connect two temporal dimensions are such as and ,


- acts as "an age of the Object",

to opposite

- is a span of time.

By the way, the astronomer Halton Arp was suggesting in his works [4] and [5], the following statements, which he made without any mathematical justification:

- That the Red shift (i.e. the effect of the red shift ) is not the manifestation of the Doppler's effect.

- The red shift effect is closely connected with the state of the Object.

- Halton Arp in his cosmological model has proposed to apply the age of the Galaxy as in parameter.

[4] Quasars, Redshifts and Controversies by Halton Arp Interstellar Media Cambridge University Press, 1987.

[5] Seeing Red: Redshifts, Cosmology and Academic Science by Halton Arp Apeiron, Montreal, 1999.

4.3 "Gravitational lenses"

Now we will tell you about a remarkable manifestation of the property of space-time - it is the so-called "gravitational lens", in accordance with it, the astronomers make the calculations of the mass of "Dark Matter".

For that purpose we use once again the above-mentioned formula. Here is it:

Let's look from the another point of view upon this new property of the space-time, in order to check-up the accuracy of the given above formulas.

What is it turns out? The volume is decreasing and the time is slowing (the increasing of time). Here we are "seeing" in the whole most characteristic features of "the curved space" (of the deformed space), which it is acting as a denser optical medium against to our space (not deformed space). We should explain that the n is the refraction coefficient. It is ratio of electromagnetic constant c to a velocity of light in medium .

In other words, light goes more slowly in denser optical medium than in vacuum. That is, the light will be overcome the same distance in denser optical medium for longer time. Therefore, we can imagine a refraction coefficient n as a ratio of two's span of time.

- Here is - a span of time, which would be required to the light to overcome the certain distance if it (the light) moved in vacuum;

- Where is - a span of time, which would be required to the light to overcome the same certain distance in denser optical medium.

And now we take a short historical digression. Let's remember about the triumphant experience, in which the english astronomer Arthur Stanley Eddington observed the Total Solar Eclipse in 1919 and respectively confirmed the correctness of the conclusions of the General Relativity Theory (GR).

...One way to check the conclusions of GRT about the distortion of space-time near Massive Bodies is the study of the deviation of a light ray passing near the Sun. One photo of the star sky have been done during a solar Eclipse, and the other six months later of the same part of the sky. Then these pictures are being combined and matched for determining the apparent displacement of stars...

"...The shift of some hundreds positions of the stars were measured and it turned out, that a deviation of light is equal 2" on average. The General Relativity this value is predicted as 1,75"...".

This experiment has certainly proved the prediction of GRT as is truthful to but remained the undefined 0,25" of the beam deviation which has not found its explanation when this epoch-making experiment was carried out. (So, the author of this article with his theory, which you the dear reader can read now, seriously pretends to this "bonus" 0,25").

Let us recollect from the school course of physics that the refraction coefficient n, is the ratio of a sine of the light angle to a sine of the angle of refraction . (Picture 3)

How to measure up these angles? We shall consider that nearby upon the surface of our nearest star i.e. on the surface of the Sun is exists so-called "curved" space. A light beam from that distant star goes on the tangent to surface of the Sun. Thereby an incident ray is coming at an angle of ninety degrees, (horizontal i.e. is at angles ). (If the light beam would enter at right angle to a surface i.e. vertical, angle would be equal to (the zero degrees)). In our case, the light beam enters to surface (at the angle ), and goes from its surface but smaller than under a right angle .

Now we shall count the difference between of these two angles. As we know, the sine value of the angle is equal to 1.


Here are:

- is the relative emission power of our Sun.

- is a "life time" of the Sun

- is the very thing deviation which earlier has not found its explanation.

5. Objects are in the Universe

5.1 "Hot" and "Cold" Objects are in the Universe

Let's have a look at this so-called "new" property of the space-time which "finds its reflection" when doing the observation for the Objects of the Universe. In order to making the better presentation of the next part of the narration, we have invented such terms as "Hot" and "Cold" Objects:

- We shall name by the "Cold" Object, which having a value of the relative emission power as such our Sun has.

- However, we will use the name of the "Hot" ones for the Object which are having a value of the relative emission power as Quasars, for example is the Quasar 3C 273.

By the example of our nearest star - the Sun, we will do the following: we will divide a numerical value of the Solar Luminosity which is expressed in watts by a numerical value of the Solar Mass which is expressed in kilogram accordingly, thereby we will find the value of the specific power - .

Evidently the value of this Specific Power is not so big the household electric heaters have much higher a values of its. This value of the Specific Power which can be compare with warmth which is produced out from the fallen leaves, which are been collected in heaps after the autumn fall of the leaves.

For comparison, we shall result the characteristics of one well-known Quasar 3C 273:

- mass - Solar masses,

- luminosity - Watt.

Just as in an aforecited example, we shall find the value of its Specific Power:

Further, if the value of the Specific Power to multiply on the multiplier, which is equal to an inverse square of a value of the velocity of light

that we shall receive H which is the value of the relative emission power:

So that and , is the dimension of the relative emission power is - minus second

Both the value of the Specific Power and the value of the relative emission power differ between themselves by only at a constant factor is

For instance, for our Sun is having the value of the relative emission power:

For the Quasar 3C 273 - is having the relative emission power:

5.2 The Hubble's constant

Now we will consider the Hubble's constant (or the Hubble's parameter). On average, the Hubble's constant has its numerical value:

Let's divide kilometers per second on Megaparsec, thereby we shall receive the

The dimension of the obtained expression is - a minus second.

Comparing an earlier received values of:

The value of the relative emission power for our Sun, the Quasar 3C 273 and Hubble's constant, one's possible dare to say, that the Hubble's constant, in its deep essence, expresses a mean value of the relative emission power of the Universe.

What is "a mean value of the relative emission power of the Universe"? For this purpose, let's perform a rough calculation, which in no circumstances, one's should not to been estimated precisely.

Let x - are a number of the "Cold" Objects in the Universe, which are similar to our Sun, are having the value of the relative emission power .

Whereas y - are a number of the "Hot" Objects in the Universe, which are similar to the Quasar 3C 273, are having the value of the relative emission power

Let's make a ratio for these values:

In our case, the value of the Hubble's constant will represent itself as the mean value, which has been compiled from the mix of value for the "Cold" and "Hot" Objects. From the aforecited expressions, let's find a numerical ratio between a number of the Objects which are similar to our Sun and a number of Objects which are such as the Quasar 3C 273. Here are:

An according to this estimation we see that a number of Quasars (and the "Hot" Objects similar to Quasars) in the Universe should make not less than 3% from total number of all objects in it. Nevertheless an astronomical observations show us, such a number of these objects are much less.

Is it time to invent the Dark Matter for ourselves?

5.3 An explanation of the paradox of a "disappearance" of the Objects

What is the matter? The matter of the fact, all these "hot" objects also are yet "the super heavy" ones. These all objects have ceased to be visible! The paradox consist in that - an Object radiates enormous number of energy; but instead of it, an Object is not visible! How should we understand it!

To explain this paradox we use such a method as analogy. (Ones shall notice, that the analogy is not exact the mathematical proof, only a direction of thought so quite suitable in given article).

Let's bring formula of an imaginary velocity . For this purpose, in the Hubble's law which shows us - the radial velocity of "the Galaxy (of the Object) which has been measured by means of the effect of red shift is proportional to the distance up to it", we make some operations.

Let's replace the value on the expression , i.e. - and let's substitute it in this formula, in the next step we substitute the Hubble's constant instead the value of the relative emission power H, in a result we shall receive:

Let's write down also one more formula from a school course of Physics. These are wellknown simplest formula, which tie together up the value of rate of movement with the value of acceleration of this object:

Here is:

- velocity (rate of movement),

- acceleration,

- time.

How in our case we shall find acceleration? For it, let's multiply the value of the relative emission power H upon a multiplier c (c the velocity of light in vacuum).Then we shall receive an imaginary acceleration of the Object, with which it is moving away from the Observer.


- is a radial velocity of an imaginary moving away of the Object from the Observer,

- is an imaginary acceleration of the Object.

For our triples of values are the following:

Right now, we shall ask a question - how much time is needed to any object which is moving with such "acceleration" can achieve of the value of velocity of light? Any object becomes invisible for observation on reaching the velocity of light, as we know, i.e. it "will disappear" from "field of vision".

For a finding the value of time of this object - we shall divide the value of velocity of light upon the value of acceleration of this object.

As may be seen from these calculations, the value of time is equal to the reciprocal value of the relative emission power H. Let's make the following calculations for our "triples" of objects: