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UKRAINE

Kharkiv

Spacetime & Substance
International Physical Journal

Volume 2, No. 5 (10), 2001

c 2001 Research and Technological Institute of
Transcription, Translation and Replication JSC

Spacetime & Substance International Physical Journal

Certicate of the series AB, No. 4858, issued by the State Committee for Information Policy, TV and Broadcasting of Ukraine (February 12, 2001).
The Journal is published by Research and Technological Institute of Transcription, Translation and Replication, JSC, ander Licence of the series DK, No. 184, issued by the State Committee for Information Policy, TV and Broadcasting of Ukraine (September 18, 2000).

It is a discussion journal on problems of theoretical and experimental physics in the eld of research of space, time, substance and interactions. The Journal publishes: | the theories combining space, time, gravitation and others interactions (including the Einstein's SR and GR); | application of theories for description and/or explanations of properties of the Universe and microcosmos; | mathematical models and philosophical bases, which touch the description of a physical reality; | description of set-ups aimed at the realization of fundamental physical experiments and the forthcoming results; | discussion of published materials, in particular, those questions, which still have not a correct explanation.

The volume of one issue includes 48 pages. Format is A4. Periodicity of the publication: quaterly in 2000; monthly since 2001. The language is English. The equivalent versions: paper and electronic (*.TEX, *.PS, *.PDF).

Editorial Board:

N.A. Zhuck (Kharkiv, Ukraine) P. Carlos (Rio de Janeiro, Brazil) P.G. Niarxos (Athens, Greece)

| Editor-in-chief

M.J.F.T. Cabbolet

V.I. Noskov (Moscow, Russia)

V.V. Krasnoholovets (Kyv, Ukraine) (Eindhoven, Holland)

V.L. Rvachev (Kharkiv, Ukraine)

| Vice Editor

P. Flin (Krakow, Poland)

S.S. Sannikov-Proskurjakov

M.M.Abdildin (Almaty, Kazakhstan) J. Gil (Zielona Gora, Poland)

(Kharkiv, Ukraine)

L.Ya. Arifov (Simferopol, Ukraine) N.D. Kolpakov (Kharkiv, Ukraine) V. Skalsky (Trnava, Slovakia)

Yu.A. Bogdanov (Kharkiv, Ukraine) I.Yu. Miklyaev (Kharkiv, Ukraine) R. Triay (Marseilles, France)

B.V. Bolotov (Kyv, Ukraine)

V. Mioc (Bucharest, Romania) V.Ya. Vargashkin (Oryol, Russia)

M. Bounias (Le Lac d'lssarles, France) Z.G. Murzakhanov (Kazan, Russia) Yu.S. Vladimirov (Moscow, Russia)

J.L. Buchbinder (Tomsk, Russia) Lj. Nesic (Nis, Yugoslavia)

(The list is not nished)

Technical assistants: V.V. Moroz (LATEX), A.M. Varaksin (Internet)

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c 2001 Research and Technological Institute of Transcription, Translation and Replication, JSC


Spacetime & Substance, Vol. 2 (2001), No. 5 (10), pp. 193{210
c 2001 Research and Technological Institute of Transcription, Translation and Replication, JSC

QUASARS AND THE LARGE-SCALE STRUCTURE

OF THE UNIVERSE

N.A. Zhuck,1 V.V. Moroz, A.M. Varaksin

Research and Technological Institute of Transcription, Translation and Replication, JSC Box 589, 3 Kolomenskaya St., Kharkov 61166, Ukraine

July 23, 20012

Regularity in quasars allocation earlier unknown revealing that the quasars are grouped in thin walls of meshes

with the medial size about 50{100 Mps, which like a foam homogeneously ll all apparent part of the Universe is

determined. For investigation the database on 23760 quasars was used, in which two angular coordinates ( ; ')

and redshift of radiation spectrum (z ) for each quasar are submitted. Distance up to each quasar by redshift was

dinevteesrtmigianteidonbyoffoqrumausalarsrsp=atRia0llnd(is1t+ribzu)t,iwonheirne

sRph0eirsictahleacnodnsctaarnttesfioarnthcoe-Uorndiivneartsees,

which equal about 1026 m. Next, is carried out. The Universe part

most explored with the help of telescopes and radio telescopes were chosen for this purpose. Delone triangulation is

carried out for laminas which thickness is appreciably less than the revealed meshes of large-scale quasar structure.

The statistical processing of the nding distances between quasars is executed. The investigations have shown

that: for large distances (noticeably are more than 100 Mps) quasars in the chosen part of the Universe without

dependence from distances and angular standing in space have averages of distribution, root-mean-square diversion

and correlation factors, typical for a uniform distribution of random quantities; in smaller gauges the quasars are

grouped in thin walls of meshes (size about 100 Mps), reminding the lather; the quasars allocation in meshes

correlates with galaxies allocation; the Universe has no precise boundaries even on distance in 30{40 billions light

years. General scientic and weltanschauung signicance of discovery that it is cardinally changes our representation

about global structure and development dynamics of the Universe as a single whole to conrm the concept of the

stationary inconvertible Universe and to reject concept dynamic dilating Universe which erroneously formed in the

XXth century and taking the beginning from a so-called the Big Bang, which ostensibly has taken place of 12{15

billions years ago.

1. Introduction
At present, the ocial science adheres to the commonly accepted concept that the Universe appeared 12{15 billion years as a result of the Big Bang of the substance which had been in tremendously dense and hot state. After that the substance expanded, cooled down, split into the matter and the electromagnetic eld and formed galaxies which are believed to continue moving farther apart until now.
Such a model is based on the non-steady solutions of the Einstein equations obtained by Soviet geophysics and mathematician Fridman at the beginning of the 1920s and the concept of the exploding commencement in the dynamics of the Universe advanced by American physicist Gamov at the end of the 1940s.
The objective properties of the Universe, which allegedly conrm this model, are the discovery of the red shift in the spectra of galaxies by American astronomer Hubble in 1929 and the Cosmic Microwave Background
1e-mail: zhuck@ttr.com.ua 2Report at the scientic seminar in the Kharkiv National Technical University of Radioelectronics (Kharkiv, UKRAINE)

Radiation at the temperature 2.7 K by American radio astronomers Wilson and Pansias in 1965. It is considered that the allocation of quasars in the Universe conrms the Big Bang too (see Appendix I).
The rst discovery was interpreted by scientists as the result of the motion of galaxies away from each other and the second discovery was construed as the remainder (relic) of the electromagnetic radiation which had segregated from the initial substance and then cooled down to the said temperature during the expansion of the Universe.
The above-mentioned properties of the Universe, incidentally, are not the direct evidence of its expansion. For instance, the decrease in the frequency of light can be the result of either the expansion of the Universe or the dissipation of the energy of light when it spread at great distances, while the osmic Microwave Background Radiation can be either the remainder of the high-temperature explosion of the super dense substance or the total radiation of all stars of the stationary Universe with the said dissipation of the energy of light.
As a result of many errors, the modern ocial cosmology, in opinion of the authors, has reached the dead-

194

N.A. Zhuck, V.V. Moroz, A.M. Varaksin

lock in the development. In works [18]{[40], N.A. Zhuck (the co-author of this work) has attempted to construct alternative cosmology by digging around the foundations of physics and re-shaping its superstruction. As a consequence, a new stationary model of the Universe, which takes into account the more rened laws of physics (or their new interpretation), has been constructed (see Appendix II).
The Universe represents a giant physical laboratory, in which fundamental physical theories are veried. Cosmology is one of the tools of this laboratory. The subject of study of cosmology is the General Relativity is one of the two theories, on which the construction of modern physics (the second theory is quantum theory) is based. Perhaps it is this major role that cosmology plays in the life of mankind.
The new cosmological model is conrmed by 40 properties of the actual Universe (observations or results of experiments). The quasars are the farthest visible objects of the Universe (Appendix I). They are excellent object for investigation by means of the new stationary model of the Universe.

Table 1: Fragment of the initial database

No. RAJ2000 DEJ2000 z

"h:m:s" "d:m:s"

1 00 00 01.3 -02 02 00 1.356

2 00 00 02.8 -35 03 33 0.508

3 00 00 05.6 -27 25 10 1.930

4 00 00 09.9 -30 55 30 1.787

5 00 00 10.2 -31 59 50 1.638

6 00 00 12.0 +00 02 24 0.479

7 00 00 12.9 -02 10 25 1.450

8 00 00 16.3 -31 44 38 1.452

9 00 00 17.4 -08 51 23 1.250

10 00 00 20.2 -32 21 01 1.275

11 00 00 22.9 -02 27 15 0.590

12 00 00 23.7 +02 12 41 0.810

13 00 00 24.4 -12 45 48 0.200

14 00 00 24.8 -30 50 49 1.465

15 00 00 36.0 -31 19 25 2.013

... ...

...

...

23760 23 59 59.3 +08 33 54 0.084

2. Initial database on quasars and transformation of their coordinates

The researches of quasars were carried out not only through telescopes. The considerable interest for researches was represented the xed coordinates of already discovered quasars. The statistical researches of quasar distribution in space in increase process of quantity of discovered quasars gave the more and more interesting results.
The database on 23760 quasars was used for our investigation, in which two angular coordinates ( ; ') and redshift of radiation spectrum (z ) for each quasar are presented [41]. The fragment of an initial database is presented in Tab. 1.
Distance up to each quasar by redshift was determined by formula

r = R0 ln(1 + z);

(1)

wimhaetreelyRe0quisalcoinns1ta0n26t

typical m (see

for the Universe approxAppendix II). R0 = 1 is

assigned for calculating of distances up to quasars and

for build-up of gures.

The formula (1) is derived out of the distribution

law of light at a large distance

r

 = 0 e R0 :

(2)

It is the very important formula. We presented two derivation of this formula in Appendix III and Appendix IV.

Calculation of quasars coordinates in spatial spherical coordinates is carried out by the formulas (in radians; the corner '1 is measured from North Pole)


=

h+



m
60

+

s
3600

12 ;

(3)

'1

=

 2

'

 180

;

(4)

where

'

=

8 >< >:

'd 'd

+

'm 60 'm 60

+

's 3600 's 3600

if if

'd 'd


<

0; 0:

(5)

Calculation of quasars coordinates in spatial cartesian coordinates is carried out by the formulas (in R0 )

X = r cos sin '1;

(6)

Y = r sin sin '1;

(7)

Z = r cos '1:

(8)

In further, the database was sorted for spherical coordinates by increment of distance up to quasars and for cartesian coordinates by increment of coordinate Z (for convenience of investigations).
The preliminary investigations have shown that the observed quasars locate on the coelosphere nonuniformly. Especially it concerns those places where North Pole, South Pole and the oceans are located (Fig. 1).

Quasars and the Large-scale Structure of the Universe

195

Figure 1: Allocation of discovered quasars on the coelosphere

3. Estimation of global homogeneity of quasars allocation

Iqtuiassacorsnissidfearsetdintchraetmdeenntseidtyinorfaansgpeaotfiavladluisetsrizb=uti2on

of 3,

and then is sharply reduced for large values of redshift

(see Appendix I). Below we shall show that it not so.

Investigation of quasars spatial distribution in spher-

ical and cartesian co-ordinates is carried out. The Uni-

verse part most explored with the help of telescopes and

radio telescopes were chosen for this purpose. Delone

triangulation is carried out for laminas, its thickness

is appreciably less than the revealed meshes of large-

scale quasars structure (the multitude of lines pairing

each quasar to its nearest neighbors without their mu-

tual crossing is constructed). Thus the particular set

of distances between quasars has turned out. Further

the statistical processing of set of these distances was

carried out.
In the beginning we have separated a thin layer of the Universe in a plane of the Earth equator (plane OXY, the axis 0Z is directed to the North Pole, Fig. 2). Further we chose the most explored areas of the Universe for the analysis. Here we shall show two typical areas for an example (see Fig. 3).
The area 1 has the following sizes: X = 1:0::: 0:5, Y = 0:2:::0:3, Z = 0:03::: 0:01 (in R0). About 379 quasars are in this area.
The area 2 has the following sizes: X = 0:9::: 0:7, Y = 0:6::: 0:4, Z = 0:03::: 0:1. About 132 quasars are in the area 2.
Allocation of the quasars in the area 1 is shown in Tab. 2 and allocation of the quasars in the area 2 is shown in Tab. 3.
As have shown these investigations, average values, standard deviations and correlation factor practically

196

N.A. Zhuck, V.V. Moroz, A.M. Varaksin

Table 3: Allocation of the quasars in the area 2

Description Calculation Theory

Mean mx

-0.8062837008

-0.8

Mean my

-0.4992200605

-0.5

Standard-

deviation x 0.05747427049 0.0577350269

Standard-

deviation y 0.06059568292 0.0577350269

Linear-

correlation kxy -0,1016258970

0

Figure 2: Thin layer of the Universe in a plane of equator

Figure 3: Standing of the areas 1 and 2

Table 2: Allocation of the quasars in the area 1

Description Calculation Theory

Mean mx Mean my

-0.7307693464 -0.75 0.05896529208 0.05

Standard-

deviation x 0.1415179730 0.1443375673

Standard-

deviation y 0.1364377974 0.1443375673

Linear-

correlation kxy 0.1089561031

0

coincide with similar parameters of uniform distribution of random quantities, i.e. with the theory. It is impossible to term these results and results of other similar investigations as ordinary accidental coincidence. Obviously that we have the facts conrming that the quasars are distributed uniformly in the Universe, and the Universe is stationary.
Next, the investigation of quasars allocation within the concept of the Big Bang of the Universe was carried out with determining of distances to each quasar in accordance with redshift but the method generally accepted in cosmology.
The investigations have shown that at the second method of distances denition:
a) quasars density grows to the Universe boundary which restricted by radius 12{15 billions of light-years, it correspond to the theory of Universe expansion from more its dense state in the past;
b) meshes in which walls the quasars are concentrated not only change in size, but also that most important, are deformed (are 
attened) as approaching to the Universe boundary that cardinally contradict to the theory of the explosion for which is typical the homogeneous expansion of a substance and, accordingly, proportional expansion of the sizes of the indicated meshes.
Thus, the second method of distances denition to the quasars and theory of the dilating Universe, from which this method follows, is necessary to consider erroneous, not relevant to the laws of physics and the observed phenomena of nature.
4. Estimation of local inhomogeneities in quasars allocation
The Delone triangulation is a set of lines pairing each quasar with its nearest neighbouring quasars. These lines not intersect and to form the delta circuits. From here the name of the triangulation method was formed.
The Delone triangulation allows to determine all distances between quasars in thin area of the Universe (i.e. practically on a plane). Further the statistical

Quasars and the Large-scale Structure of the Universe

197

Figure 4: Delone triangulation in the area 1

Figure 5: Histogram of the interquasars distances

handling of multitude of these distances is carried out that allows to obtain objective appraisal of large-scale allocation of quasars in the Universe, and also to determine structure of the Universe as a whole. After that the initial model of the Universe is conrmed or rejected.
We shall show for example how the Delone triangulation method for area 1 was used. We shall remind that about 380 quasars are in this area. Thus about 750 distances between quasars is formed provided that the lines between quasars are not intercrossed (see Fig. 4).
Further we have constructed a histogram (Fig. 5). Here density of quasars dN is put aside on a vertical axis. Distance between the nearest quasars is put aside on a horizontal axis. The histogram shows that
tq=hue3en.d1tilsy1t.0a1nT6caemksi,nrtgdhNiinsmtadoxisa=tcacn0oc:u0en2it4sRtehq0autcaolRma0beoauc1tr0o7s7s2.46mMmosp,ts1f.rpeIst-
practically is equal to diameter of Universe honeycomb, which is estimated approximately in 50{100 Mps.
It is obvious, that on the obtained histogram the greatest distances (more than 0.1{0.15 radiuses of gravitational interactions) should generally be excluded from the analysis, as they are interlinked with edge eects, i.e. that the isolated part of the Universe without the taking into account of presence of neighboring quasars was considered.
5. Discussion
The analysis of the received results has allowed to decide that:
I. The new method of distances denition (1) up to quasars does not contradict observed phenomena

and common sense, quasars in cosmological gauges distributed uniformly, and in smaller gauges form a foam mesh structure of the Universe with the size of meshes about 100 megaparsecs.
II. The old method of distances denition up to quasars gives the results, which contradict known standings of the explosion theory and common sense. Therefore, concept of the Big bang of The Universe is also untrue.
III. The accepted results of the astrophysicists are untrue asserting that the quasars concentrate on particular distances and are typical for a particular period of the Universe life, as in their investigations the general dependence of quantitative density of quasars on distance was considered, but their spatial distribution, inhomogeneity observation of sky both on corners, and on distance up to quasars was not taken into account.
6. Conclusion
The investigations have shown that: a) for large distances (noticeably are more than 100
Mps) the quasars in the chosen part of the Universe without dependence from distances and angular standing in space have averages of distribution, root-meansquare diversion and correlation factors, typical for a uniform distribution of random quantities;
b) in smaller gauges the quasars are grouped in thin walls of meshes (size about 50{100 Mps), reminding the lather;
c) the quasars allocation in meshes correlates with galaxies allocation;
d) the Universe has no precise boundaries even on distance in 30{40 billions light years;

198

N.A. Zhuck, V.V. Moroz, A.M. Varaksin

e) asserting that the quasars concentrate on particular distances and are typical for a particular period of the Universe life is untrue;
d) the Universe is stationary system. General scientic and weltanschauung signicance of discovery is that, it cardinally changes our representation about global structure and development dynamics of the Universe as a single whole to conrm the concept of the stationary inconvertible Universe and to reject concept dynamic dilating Universe which erroneously formed in the XXth century and taking the beginning from a so-called the Big Bang, which ostensibly has taken place of 12{15 billions years ago. The discovery conrms revealed earlier by one of the co-authors N.A. Zhuck the physical laws of the Universe functioning and competence of their practical use for cognition of the world and practical needs of a man.
Appendix I GENERAL INFORMATION ABOUT QUASARS
Investigations of the Universe through radio telescopes have resulted in discovery such surprising objects as quasars. The increased resolving ability of radio telescopes has served as the background of quasars discovery. It has allowed dening the coordinates and angular sizes of objects emitting radio waves with more accuracy than earlier.

corresponded to very hot objects with ultra-violet excess.
By 1962 T. Met'juz and A. Sandage have identied with star-shaped objects the radio emission sources 3C 196 and 3C 286. 1963 became decisive, to this time of K. Hazard, M. Makkej and A. SHimins with record accuracy determined the coordinates of radio emission sdeoaisucthracnescoe3uCrbcee2t7wle3es.esnT10cho0e0m.opObojnenecetnothfsasisonuarp1c9pe0e0caoarmenddpoddnoieaunmbtlseetceworiitnoh-f cided with "feeble star" (mV = 13m ). Young Dutch astrophysicist Maarten Schmidt on observatory Mt. Palomar has investigated the spectrum 3C 273, in which again there were incomprehensible emission lines. Just he has supposed that these lines can be identied with the Balmer hydrogen line if to admit redshift equal 0.158.
The correctness of line identication oered by Schmidt was proved by Dj. Ouk, which has found in the infrared spectrum 3C 273 line H in accuracy on that place where it should be with oered value of redshift. After the specied event T. Met'juz and Dj. Grinstejn identied lines in the spectrum 3C 48 having supposed redshift z = 0:367.
Nine such objects became known to the end of year and then the 
ow of discovery has gushed when became clear on what attributes is possible them to search. By 1967 was already found about 150 quasi-sidereal radio emission sources (quasistellar sourse, QSS), in 1977 them became 370 and very soon the name quasar (for such objects) was coined.

Quasars discovery

Two 27-meter antennas of the California technology in-

stitute which locate in Owens valley represented in pair

with each other the radio interferometer have begun

coordinates measurement of the radio emission sources

which have been recorded in the 3rd Cambridge cata-

logue (3C) in mination has

r1e9a6c0h.edThe50a0 cacnudraacsy

of coordinate deterresult measurements

was discovered that some sources have the very small

angular sizes.

September 26, 1960. T. Met'juz and A. Sandage

have photographed on a 200-inch telescope of the sky

area containing one of such sources 3C 48. Within a

rectangle of coordinates errors in this area there were no objects except for the star 16m; 2V . Around the star

there were tracks of feeble nebula but the object looked

star-shaped. October 22, 1960. A. Sandage has inves-

tigated a spectrum of the discovered object, in which

there was a strong combination of broad emission lines,

which was impossible to identicate. Any of spectral

lines was not possible to know in its spectrum, lines

was not possible to identify no with one chemical ele-

ment. The color indexes 3C 48 were unusual too, they

Basic observed properties of quasars

The quasars at observation through a telescope look

like as star-shaped objects, which besides are strong

sources of radio emission. They have excess of radiation

in ultra-violet and infrared area of a spectrum. Spec-

trum contains broad lines of radiation, always strongly

shifted in the red side.

The quasars have a number of surprising properties:

a) The extremely

gpreoawterfroomf th1e0i3r7

eulepcttroom10a4g0neWti.c

radiation is For compar-

ison we shall specify that the power of radiation of our Galaxy amount approximately 1037 W. It is supposed,

that this high-power tional collapse of huge

rwaediigahtitofnrocman10a6riusep

at to

1a0g10raSvoitlaar-

weight;

b) The spectrum of radiated light nds out strong

redshift characterized in parameter z = /, where

 - wavelength of observation light, and  - its red-

shift in the side of long waves. This redshift is so great

that, for example, the line  of series Lyman in a hy-

drogen spectrum, at standard conditions observed in

ultra-violet area, appears in a visible part of a spec-

trum;

Quasars and the Large-scale Structure of the Universe

199

c) The quasars change their brilliance, at some the oscillation frequency of brilliance reaches up to 3m and

more. For example, the quasar 3C 279 has the ampli-

tude amount almost 7m and in a maximum of brilliance

it is one of the brightest objects of the Universe, its

MB = 31m; 4;

d) Feeble nebula ambient quasars were discovered,

radiation of nebula so feeble, that for their ephemer-

al view the English and American astronomers named

them beautifully as \fuzz". So, in the center of such

\fuzz" which is the size of a giant galaxy, a quasar like

dense, tiny corn of a poplar in its shell is located.

The energy-release of quasars is huge. The luminos-

iatbyoouftou10r3G7 aWlax; ythaes

was already mentioned amounts to quasar luminosity on some orders

is higher. Total energy emitted by quasars is estimated in 1054 watt-second. It is in 10 billions times more

than the Sun has emitted for all time of its existence.

Variability of quasars radiation is found out both in op-

tical and in a radio-frequency range. The oscillations of

luminosity occur in times by an irregular mode about

one year and less (up to several days). Therefore, it is

possible to make a conclusion, that the sizes of quasars

do not exceed a route transited by light during essential

change of luminosity otherwise variability would not be

observed. Hence, it is indirectly possible to estimate the

sizes of quasars, their diameters do not exceed one light

year, i.e. the quasars are smaller even of single galaxies

(For comparison the diameter of our Galaxy about 100

thousand light years). From here follows that all the

huge energy of a quasar is generated in an insignicant

small volume.

Starting from such observed quasars properties sev-

eral guesses were made:

Either

1) Or these objects located very much far outside a

Galaxy and luminosity of objects in 100 and more time

exceeds a luminosity of giant galaxy,

2) Or the quasars are objects thrown out from a

kern of a Galaxy with tracks of explosive activity of

kerns and moving with huge velocity, then distance up

to them can be estimated by value about 106{107 par-

secs, hence, and these objects radiate much less energy.

In the beginning the observed redshift tried to ex-

plain at the expense of Doppler eect. Then the quasars

should 
ee from us with huge velocity. Quite often

therefore it is possible to meet in the literature the

identication Doppler shift

of z

=thpe p(1ar+amu/ect)e/r(1z

with the relativistic u/c), which comes

on change to nonrelativistic Doppler shift z = u/c,

when the relative velocity u becomes close to veloci-

ty of light in vacuum c. Thus, the quasars should 
ee

from us with velocity, close to velocity of light in vacu-

um. Such explanation, however, looks rather doubtful.

Besides, the guess suggested in this connection that the

quasars represent objects thrown out by kerns of galax-

ies of a Local galactic congestion with almost velocity

of a

light removed from us no more than parsec (1 parsec = 3.26 light years =

o3n:1101m01i6llimon)s,

puts many new problems.

Today almost everyone recognizes that the shift of

quasar spectra in the side of long waves is explained not

by Doppler eect, and it generates the cosmological red-

shift. According to this explanation, the further from

us is located a quasar, the more its spectrum is shifted

in full conformity with cosmological eect of Hubble.

Cosmological models of the Universe
Any hypotheses and guesses explaining observed properties of the Universe always are formulated on the basis of denite cosmological model. Now in a cosmology there are two main models. The rst model is based on a General Relativity (GR) and named as the model of observed Einstein-Fridman Universe. The second model was oered by such scientists as Bondy, T. Gold, F. Hoil and named as the model of the stationary Universe.
In both models is recognized that the large-scale structure of the Universe is identical everywhere and in all directions, i.e. the Universe is homogeneous and isotropic. But \the Perfect cosmological principle" the theory of the stationary Universe says that, besides that the Universe is identical not only everywhere, but also always. In the theory of observed Einstein-Fridman Universe there are solutions of two types. According to rst, the Universe is dynamic and is continuously dilating after a so-called The Big Bang (the moment of the Universe birth). In the second version the expansion slows down more and more, and then will be replaced by squeeze and the Universe will be squeezed to a condition of extreme large density (condition of a singularity), and then again expansion will begin.
Today, the cosmological model of Einstein-Fridman is traditional and universally recognized and all explanations of observed properties of the Universe are created, as a rule, on the basis of the specied model.

Hypotheses about a quasars nature within the framework of conventional cosmological model
Quasars as dened stage of the Universe development The statistical analysis of quasar redshift has shown that the values z in general do not exceed dened val-
ue z  5:5 and shows the tendency to concentrate in
an interval from z = 1 up to z = 3. In the beginning this is explained that because of absorption of light in interstellar gas the farther objects are inaccessible to modern telescopes. However, later the other explana-

200

N.A. Zhuck, V.V. Moroz, A.M. Varaksin

tion was put forward. According to it even with the help of more perfect
telescopes dilating horizons by the observed Universe which allow to glance in its farther past, it is impossible to discover new more remote quasars since before the dened moment they simply did not exist. And this moment already now is within the reach of our telescopes. According to this cosmological interpretation since the radiation received by us from quasars today goes up to us about 10 billions years then the researchers observing the quasars is looking in the past of the Universe on 10 billions years back. The Universe then was at earlier stage of development and the processes taking place in its, diered by huge energies. It also explains unusual power of quasar radiation.
Starting from such guess, it is possible to consider, that the quasars correspond to a dened phase of development of the Universe as a whole, and are a characteristic feature for its, far past. Accordingly, up to quasars existing on early phases of the Universe development there should be huge distances, which the observations conrm. Con
uence of galaxies as the reason of a quasars phenomenon Observations and researches of the \fuzz" images around quasars have resulted in new discovery. It is discovered that many of the \quasars" galaxies interact with other galaxy. Percent of such pairs is rather high and it reaches 30 % in the systems with small redshift [11]. Such facts observed allow to suppose that phenomenon of a quasar in many cases can be aroused by the galaxies interaction.
The specied hypotheses are that the interaction of galaxies strongly perturbs motion of gas in a system, and it falls to the center of a galaxy. There, a supermassive black hole \gobble up" it and this process is accompanied by liberation of huge quantity of energy, which we observe as a phenomenon of a quasar.
The modern researches show that the processes of con
uence galaxies and the processes of activity of galactic kerns correlate among themselves. In this connection it is possible to suppose, that the epoch of quasars formation can be simultaneously by epoch of formation of massive galaxies at the expense of merging less massive units (dwarf galaxies). Straight observations of master's galaxies (galaxies, which swallow up other galaxy) the nearest quasars through the Hubble telescope have given conrmation of straight connection the activity with interaction and con
uence of galaxies. In particular, in case of master's galaxy of quasar PKS 2349 is discovered that the satellite galaxy of a scale BMO is immersed in its.
According to the above-stated the quasars represent a rather complicated accretion system around a supermassive black hole located in the center of a mas-

ter's galaxy. It is so-called accretion disk and a shaded disk or thick disk on which axis the radiolet is directed in case of radioloud objects, the system of fast 
ying clouds, which shape broad optical emission lines, and on large distances behind a disk give narrow optical emission lines.
Similar \assembly" of galaxies is observed with the help of the Hubble telescope on redshift about 2{3. Such process can explain both as fast decrease of number of quasars from the past to the present and wellknown rupture in their distribution on large redshift. The radioloud quasars in model of con
uence communicate with the rotation of a black hole, which is initiated or recent \strong" con
uence of a comparable weight galaxies or rather small quantity of "feeble" con
uence of a massive galaxy with dwarfs. Besides it is considered, that the con
uence lead to occurrence of activity of galactic kerns. Quasars as a dened phase of a galaxy life Many characteristics of quasars are observed and at galaxies, i.e. between quasars and galaxies there is a continuous connection. Such galaxies reveal in the spectrum strong ultra-violet excess, some have appreciable redshift and are not sources of radio emission. The brightness of galaxies are much less than quasars. The radio emission was also found in some galaxies they were named by N-galaxies.
The spectra of quasars are similar to spectra of kerns Seyfert galaxies that in the eld of the kern have broad emission lines indicating on the motion of large mass of gas. The energy distribution in a spectrum is also similar. The characteristics both radio emission and polarization of quasars light and galaxies dier from each other a little. The high-power 
ows of infrared radiation are observed both from quasars and from kerns Seyfert and radio galaxies. Therefore, hypotheses were put forward that the quasars are active and superpower kerns of remote, young galaxies.
Especially important and convincing evidence of nature unity of quasars and galaxies was the detection in 1967 by Dj. Ouk of brilliance variability of a unobstructive radio galaxy 3C 371 with amplitude about 2m . The brilliance variability of several N-galaxies and Seyfert galaxies soon also were discovered. It turned out, that the brilliance variability is not a unique property of quasars, and this property is peculiar to galaxies with an active kern.
The likeness of quasar properties with properties of kerns Seyfert galaxies has given the basis to assume that the quasars are kerns of young galaxies.
More late observations in the beginning of 70's and in 80's years of XX century have shown that the discovered feeble nebulas around quasars in color are similar to late blue spiral galaxies and sometimes are even bluer. The blue color of galaxy indicates upon plenty

Quasars and the Large-scale Structure of the Universe

201

of young massive stars. It can mean that a nebula represents a young galaxy in which there is a high-power process of star formation.
In 1982 the American astronomers T. Boroson, Dj. Ouk, K. Grinss could found a good spectrum of nebula around quasar 3C 48 and have found in it, a narrow, typically stellar line of magnesium absorption. It was the rst direct proof that the quasars are surrounded by stellar component and they are possibly considered as kerns of born galaxies.

Conventional representations about quasars distribution in space

Detection chronology of new quasars, a ways of their search

Since the moment of discovery the quantity of the detected quasars is constantly increased. In process of perfection of technical and methodological means of search and identication it is discovered more and more far quasars. But if to analyse the detection chronology of these objects then the next feature of quasars comes to light.

From the moment of quasars discovery in 1963 the process of detection of new quasars went very fast, but after achievement by redshift of value z = 2 dynamics of this process was considerably slowed.

If to analyse technical ways of quasars detection, it is possible to see, that at rst mainly the radioloud quasars are discovered then since 1965 radiosilent quasars are discovered. They are discovered as blue objects, using the test of \ultra-violet excess". But such technique of quasar detection becomes inecient at values of redshift exceeding 2 and this fact could explain slowing down the rates of discovery of new quasars.

At the end of 80's of XX century new more eec-

tive optical techniques of quasar detection have ap-

peared. It has allowed in the rst time, to discover

quasars with large value of redshift. But, despite of

large-scale researches with application of modern tests

of detection and identication it was very dicult to

nd quasars with redshift exceeding 5.5. The question

emerges whether it is possible to discover quasars with

large value of redshift. Despite of limitations in mod-

ern methods of detection the quasars in general should

be discovered at values z > 5:5. Such situation has re-

sulted in the guess that on farther distances the quasars

practically do not meet. And density of a spatial distri-

bz u=tio2n

of 3

quasars is , and then

fast incremented in is sharply reduced

range of for large

values values

of redshift (see Fig. I.1).

Figure I.1: A relative spatial density function of quasars
Periodicities in quasars spectra
The researches of quasars were carried out not only through telescopes. The considerable interest for researches was represented the xed coordinates of already discovered quasars. The statistical researches of quasar distribution in space in increase process of quantity of discovered quasars gave the more and more interesting results.
The researches of quasar distribution were carried out on dierent parameters including on value of redshift z . Thus in general, histograms of distribution are built, explored peaks in quasar distribution especially nearby z = 1:95, but the further statistical analysis, as a rule, was not carried out.
The correlation analysis of a histogram of quasar distribution was carried out in 1971 by Carlsonn [9, 10], who has revealed qualitatively new feature of distribution of quasars in space, the periodicity of distribution on argument ln (1 + z). Calculation of an auto correlation function has conrmed presence of the specied periodicity. The sample of 166 objects was explored, and the period P on argument ln (1 + z) has made 0.205.
Such fact, in a spatial distribution of quasars on redshift required an explanation, and originally reason of occurrence such irregularity was seen in techniques of quasars detection (eects of selection). But in the further the conclusion about strong in
uence of eects of selection was doubted and the objections against nonuniformity in distribution of quasars on ln (1 + z) were rejected.
The statistical researches of coordinates of discovered quasars were continued, the more and more new samples, for a lot of objects were under construction, but the result remained the same, the redshift of discovered quasars tended to avoid some intervals z .
Today, the researches of periodicity in a spatial dis-

202

N.A. Zhuck, V.V. Moroz, A.M. Varaksin

tribution of quasars are continued, but precise physical interpretations within the framework of conventional cosmological model of the Universe have not obtained.
Conclusion
Any facts observed should be liable to careful understanding and what obvious was this or that fact always there should be a dened shadow of doubt in the validity of interpretation of this fact.
As it was possible to see, within the framework of the traditional cosmological model there are enough of diculties and contradictions at interpretation of discovered properties of the actual world.
Appendix II MODEL AND PHYSICAL LAWS OF THE UNIVERSE Introduction
The Universe is the study subject of cosmology. Cosmology is the general part of mathematics, physics, astronomy and philosophy, which studies the structure, evolution, and physics laws of the Universe as a whole.
The integral notion about the Universe puts cosmology in a special position in relation to other sciences. Indeed, if any other science can study its subject fully and comprehensively the investigator of the Universe can only examine part of the subject. Since the whole can exhibit such characteristics which are not present in its parts, the diculties cosmology has been facing at all times can be understood.
The essence of the diculties has always been as follows: any physical theory could not fully explain the observed properties of the Universe. If the theory was somehow adjusted to describe some properties of the Universe, the consequence that emerged did not agree with other known features or fell outside the common sense.
The situation is also aggravated by the fact that the Minkowski space-time in the General Relativity [2, 3], which represents the theoretical foundation of modern classic cosmology, is described by ten variables, while the theory itself oers only six independent equations. Therefore, it is no wonder that no one could construct an objective pattern of the world yet based only on the equations of the General Relativity.
As a result of discrepancies in the theory, particular hypotheses needed to be advanced to explain certain properties of the Universe. For this reason, many different models of the Universe have appeared. Unfortunately, no one of them fully satises all the requirements of the laws of logic or conforms to the real world.

At present, the ocial science adheres to the commonly accepted concept that the Universe appeared 12{ 15 billion years as a result of the Big Bang of the substance, which had been in tremendously dense and hot state. After that the substance expanded, cooled down, split into the matter and the electromagnetic eld and formed galaxies, which are believed to continue moving farther apart until now.
Such a model is based on the non-steady solutions of the Einstein equations obtained by Soviet geophysics and mathematician Fridman [4, 5] at the beginning of the 1920s and the concept of the exploding commencement in the dynamics of the Universe advanced by American physicist Gamov [6] at the end of the 1940s.
The objective properties of the Universe, which allegedly conrm this model, are the discovery of the redshift in the spectra of galaxies by American astronomer Hubble [8] in 1929 and the Cosmic Microwave Background Radiation at the temperature 2.7 K by American radio astronomers Wilson and Penzias in 1965 [16].
The rst discovery was interpreted by scientists as the result of the motion of galaxies away from each other and the second discovery was construed as the remainder (relic) of the electromagnetic radiation which had segregated from the initial substance and then cooled down to the said temperature during the expansion of the Universe.
The above-mentioned properties of the Universe, incidentally, are not the direct evidence of its expansion. For instance, the decrease in the frequency of light can be the result of either the expansion of the Universe or the dissipation of the energy of light when it spread at great distances, while the osmic Microwave Background Radiation can be either the remainder of the high-temperature explosion of the super dense substance or the total radiation of all stars of the stationary Universe with the said dissipation of the energy of light.
The question about the model and the laws of the Universe is comparable with a problem of what is prime: an egg or a hen. So if we dene cosmology as the science about the Universe, we are immediately facing the problem of what is initial: the model of the Universe from which the law of physics of the Universe follow, or the laws of physics of the Universe, on the basis of which the model of the Universe is constructed?
Apparently, the problem does not need a direct answer. However, a third question, which is as if a quasisuperstructure over the dilemma about the primacy of the model or the laws of the Universe, requires resolving. The point is about the proportion and interrelation of such philosophical categories as the \whole" and the \part" and also the philosophical law of quantitative changes passing into qualitative changes. Here again, strictly parallel movement is needed.
To study the whole by its part, it is important to have continuous integration of notions on the subject of

Quasars and the Large-scale Structure of the Universe

203

Figure II.1: Systems of readout

the investigation from dierent points of view at every stage of its investigation and continuous coordination of outcomes of the theory under development with the objective reality. Non-observance of the principle of conformity, occurrence of internal contradictions, singularities and paradoxes while applying the given theory for the description of the whole indicates to the falsity of the way taken by the investigators. It is the very situation, which has developed in cosmology nowadays, its ocial theoretic ground being based on the idea of Big Bang.

Light speed is a tensor

Any observer can not simultaneously be in several sys-

tems of readout. This fact guesses viewing all the nat-

ural phenomena only in one inertial system of readout.

Thus there is a problem what is the speed of light of

rather propellent objects.

twoCinoerrreticatllysytsoteamnsswoefrrethadisopurtoKble, mK, 0waensdhbalolucnodnswiditehr

them two rulers, as it is shown in a Fig. II.1.

andLqe0t

at that moment, when the beginnings coincide with each other, the bulb in

of rulers q a point q ,

bound with a xed ruler, will light up. In time t light

will reach a point S on this ruler. For the same time the

relative S there

frame ruler will will be a point

mS0o.veTahnuds

on the contrary point distance, which light

has passed along a relative frame ruler on quantity vt

will be less than distance which it has passed on a xed

ruler. Hence, observer who is taking place in a point

S (that is in xed system of readout) on the gauges of

soropufpalpaecorleisgwiathneittdhdwtiraivmeveceletoicscoahinttoycwuhleicdls0l mub=peakarceepcaeoidivvnee.tdduSAcc0t0tia=olanocn,mgt+hoaatvitp.ortnohpeineflrlotehnnett

All above-stated does not contradict a postulate of

a special constant

theory only in

of relativity, as inertial systems

tohferesapdeoedut,ofanlidghct0

is -

is a speed of light in one inertial system of readout

measured on gauges of space and time of other inertial

system of readout. Let's term it as a local velocity of

light.

Thus, from this point of view the local velocity of

light represents a tensor of the second rank (naturally,

Figure II.2: The tensor of light speed

in three-dimensional space) which all builders by the ends contour a ball of radius r = c displaced in relation to propellent object forward on quantity of velocity v of its motion (Fig. II.2). This ball is a geometrical fashion of a tensor of a local velocity of light [28].

The gravitation law

As it is known, Einstein has oered two views of the equations of the General Theory of Relativity which dier from each other on an addend with the cosmological term :

Rik

1 2

Rgik

=

Tik;

(II.1)

Rik

1 2

Rgik

gik = Tik;

(II.2)

wCmhroiemsrteoenRteuilkmciustrtevhnaestouRrriecocftieatnessnousrbomsrt, acRnocnlijevkow;luiTtthiikoonuitsofatthhseue beRnsitemarngacyne-of gravitational eld; gik is the metric tensor of fourdimension spacetime; R is the curvature scalar, convolution of the Ricci tensor;  = 8G=c4 is Einstein's constant; c is the light speed; G is Newton's gravitational constant; i; j; k; l = 1; 2; 3; 4.
For a unique select of the equations it is necessary to take into account some performance of the Universe. Such performance is global 
atness of the Universe which mathematical expression is equality

Rlijk = Rik = R = 0:

(II.3)

As for the actual Universe lled with substance with
de
ection density, T 6= 0, with the account (II.3)
the fact of omission of equality (II.1) becomes obvious. Thus, the 
at in global gauges Universe can be featured only with the equations (II.2). And, the diversions from 
at space-time under activity of material masses can be

204

N.A. Zhuck, V.V. Moroz, A.M. Varaksin

presented precisely (precisely!) only in a composition of

the total which corresponds to the assignment of a tensor gravitational eld hik on a background of the 
at

material world in arbitrary coordinates with the metric 
ik [7, 12, 13, 14]:

p ggik  p 
 
ik + hik ;

(II.4)

The other, not less important property of the Uni-

verse is its homogeneity and isotropy in great gauges.

Mathematicaly this property can be re
ected as equal-

ity sor

to zero density

opf

a

covariant derivative(derivative) of tenggik and corollaries of this equality (in

Lorentz's coordinates):

p ggik ;i = p ggik ;i = p ghik ;i = 0; (II.5)

where the point with comma designates a covariant derivative, and the comma is usual derivative.
After that the equations (II.2) with the help of transformation (II.4) and requirement (II.5) are given in the eld equations of the General Theory of Relativity

2hik

2 3

hik

=

2Ti0k;

(II.6)

where stance

tToi0gketihseranwietnheragysu-mbsotmanecnetuomf gtreanvsiotartioofnaal

subeld

which is oozed from the left-hand part of the Einstein's

equations. Under the same requirements in [1, 4] the

identity of Lagrangians for a deduction (II.2) and (II.6)

is proved also.

Taking into account homogeneity and isotropy of

the Universe (that is symmetry of a problem), for a

spherical-symmetrical material body of mass m the

equations (II.6) give the exterior solution as Yukawa

potential

r

' = Grme R0 :

(II.7)

The constant R0 is termed as radius of gravitational interactions and is determined under the formula

R0

=

r
c0

3 4G0

:

(II.8)

For two of material bodies with masses m1 and m2 the following law of gravitation is gained

F

=

G

m1m2 r2

e

r R0


1

+

r R0



:

(II.9)

From the analysis of the obtained law follows that in the actual Universe all the material bodies (planets, stars, galaxies) interreact with each other more feebler than it follows from the law of Newton gravitation.

Identity of inertial and gravitational masses

It is necessary to note that in linear approach the actual law of gravitation (II.9) becomes:

F



G

m1m2 r2


1

r2 R20



;

(II.10)

which shows, that all material bodies in the Universe

interreact with each other practically only in limits of

radius of gravitational interactions equal approximately 1026 m (or 20 billions of light years).

On the other hand, if to compare an actual law of

gravitation and law of gravitation of Newton, it appears

that the area under a curve of force of the actual law on
an interval from 0 up to 1 is precisely equal the areas

under a curve of the law of gravitation of Newton on

an interval from 0 up to R0. Hence, law of gravitation (II.9) valid for the actual Universe, from the energy

point of view by the law of Newton gravitation can

be replaced restricting radius of activity of forces by

quantity R0. The given approach allows to decide a series of remarkable problems promptly and obviously.

In view of above-stated we shall analyse, how the

area of interaction of a material point of mass m with

the Universe will vary at its dispersal up to velocity

v and in what all this will give. It is to show that the

new area of interaction of a point with medium also will

represent a ball of radius R0, but moved forward on a

course of its motion on quantity R0 it is necessary to substitute

cr0

(as in expression for ). It is possible also

to show that the relation is valid

r

=

v c

R0;

(II.11)

Thus, the area of interaction of a propellent mass point displaces forward on a course of a motion proportionally velocities of its motion. In a limit, that is when the velocity of a motion is equal to speed of light the propellent point should be on a surface of its area of interactions. But it just and probably only for light.
At dispersal the point m loses gravitational connection with a part of space u behind of itself and will enter gravitational connection with a part of space w ahead of itself (Fig. II.3). The sizes of the areas both are identical and depend only on velocity v , but the situation of a point m concerning them is unsymmetrical. Hence, the aggregate operation on overcoming forces of a gravitation of area u and forces of a gravitation of area w is not equal to zero.
The author managed to nd receptions of denition of this operation. If to take into account a probable initial velocity v0 a material point, for low speeds the operation has appeared to equal quantity

A

=

mv2 2

mv02 2

:

(II.12)

Quasars and the Large-scale Structure of the Universe

205

Figure II.3: Change of the interactions area at acceleration of a point

Thus, we have received, known from mechanics the theorem, of change of a kinetic energy of a body. If the obtained expression to dierentiate on velocity and on time, the second Newton's law will be received. All this is valid in a relativistic case.
Charakteristic feature of the obtained results is that both in the theorem of change of a kinetic energy, and in the second Newton's law not inertial, but gravitational mass enters so long as only such mass considered from the very beginning. So the identity of inertial and gravitational masses spirit of the Mach's principle [15] is proved and the mechanism of interaction of material bodies with the Universe is uncovered.

Gravitational viscosity and geodetic curvature of the Universe

After dispersal (cancellation of local force) of material body along coordinate X its free motion is featured by the equation

d2X dt2

+

H

dX dt

=

0;

H

=

r

4G0 3

;

(II.13)

where H is the Hubble's constant, which has absolutely other physical sense, as it is accepted in a conventional cosmology.
By presence of the second (dissipative) addend the new law of a free motion diers from the rst Newton's law. As a whole one of the most prime statements of this law can be such: if the local forces do not act on a body, the standing of its interaction area from the Universe (on the level R0) in due course does not vary, and it aims asymptotically to the centre of this area.
The new property of the Universe is termed as gravitational viscosity. As the stationary value of Hubble has the order 10 18 s 1 , the gravitational viscosity practically has no an eect for local processes (for example, in gauges of Solar system). In a distance equal

to half of medial distance between galaxies the forces of the gravitational viscosity become comparable with the centrifugal forces and answer for shaping of the medialgauge structure of the Universe, that is for shaping of galaxies.
The concept of the gravitational viscosity of the Universe adjoins by a tight fashion to the concepts of anities (parallel transport of vector) in a nonEuclidean geometry of multivariate spaces. For a motion of the nonconservative systems | that is in the general view | there is a relation for the curvature of space

Kj

(t)

=

d2Xj dt2

+

j dXl lk dt

dXk dt

=

' (t)

dXj dt

:

(II.14)

rstTkhiendm(eadianl eadcdomenpdenwditehncCyh) risjltkoineld'sicatgeusreas

of the degree

of normal curvature of space (we shall term it as geo-

metrical) in which the parallel transport of vector and

the letter on change of the length of the vector, that

is on the existence of a dissipation of energy. It deter-

mines so-called geodetic curvature of space

q
K = gijKi (t) Kj (t):

(II.15)

For the actual Universe the geodetic curvature is equal

r
K = K0 1

v2 c2

;

(II.16)

where equal

aKpp0r=oxHimcatiselcyo1n0sta1n0t

for the m/s 2 .

Universe

coecient

In the whole the analysis of all the results shows that

the motion concerning the Universe has a character of

a terrain clearance motion, but on activity of the local

physical laws it cannot be noted (except for inertia and

red bias in spectrums of radiation of other galaxies).

The propagation law of light and the Hubble's diagram

Thahseshaonwalnystihsaotfgirnatveirtaacttioionnalopfoltiegnhttiawl i(thct2h)eaUctnsiovneriste, giving power loss and, as a corollary, change frequency  in relation to initial 0 under the law.

r

 = 0e R0 :

(II.17)

The given law completely permits photometer paradox, explains a nature of red bias in spectrums of radiation of other galaxies without engaging a Doppler eect and gives a new formula of denition of distances up to galaxies

L = R0 ln (1 + z) ;

(II.18)

206

N.A. Zhuck, V.V. Moroz, A.M. Varaksin

where z is parameter of red bias of light frequency.

In view of the new law of distribution of light de-

pendence \visual stellar magnitude m | red bias z "

(the m

H=u5blbgle'ps d1i+agzralnm()1g+aizn)s

a view: + 21:68:

(II.19)

In a gamut of apparent values of stellar magnitudes

the given dependence practically is linear and completely coincides experimental datas.

The law (II.17) completely explains a nature, numerical performances and character of allocation of

background microwave radiation. Actually, it is not a relic of the Big Bang, and aggregate radiation of all radiants of electromagnetic radiation (stars, galaxies

etc.) of the Universe. If to integrate the whole ra-

diation impinging on a single site on space from zero to innitum the temperature of this radiation will be determined by the formula

T0

=

r
4

Ls

0

R0

4Ms

;

(II.20)

where Ms; Ls is medial mass and complete radiation 
ow of a medial star (or galaxy);  is the StefanBoltzmann constant.
The evaluations show, that temperature of integrated radiation is equal to several degrees above terrain

clearance zero (more precisely to calculate it is impos-

sible), as it is observed actually. And its spectrum corresponds to a radiation spectrum of an absolute black

body.

Large-scale structure of the Universe

The actual law of gravitation has a series of pleasant features. So, the evaluation of a binding energy of a material body of mass m from the Universe gives quantity

E0 = mc2;

(II.21)

which is equal precision to an internal energy of a body

taken with an inverse. In contrast to it, the law of

Newton gravitation gives a minus perpetuity. That is

why with application of a Newton's laws to the innite

Universe the gravitational paradox also has appeared.

In the actual Universe with the actual law of gravitation

such paradox does not exist, and the mass appears a

measure of connection of the given material body with

the whole Universe.

The actual law of gravitation gives one more impor-

tant corollary: with mass shown in interactions with a

material body depends on a relation of radius of a body

R to radius of gravitational interactions R0

0

M

=

R2c2 2GR0

B@1

2R 1 e R0 CA :

(II.22)

v+o1luAm)tteRo, asnudrfRaact0eRtahreemaRoa0fssa(oobfroatdhbyao.tdIiyts

is proportional to its
the same when R !
gives in a deduction

about ability of a substance to create screen eect. It

is capable to explain virial paradox and existence of

gravitational-makes of areas of the Universe.

The interesting physical sense has also radius of gravitational interactions (II.8). It appears that it corresponds in precision to radius of a black hole on which surface the speed of light is equal to the rst solar escape velocity. Thus, it is possible to tell that we live at in the centre of a black hole, but it is not our privilege, and the property of the Universe to form around of any point gravitational-makes area. By the way acceleration due to gravity on a surface of such black hole is equal only 10 10 m/s2.

On the other hand, if to unit two identical material objects in one, not changing density the mass of the obtained object shown in interactions will be less than total masses of builders. It also should be expected, as the formally given law is similar to the law of nuclear interactions in the eld theory of nuclear forces.

In classical physics there is a special theorem proving that inside a spherical-symmetrical material shell the gravitational eld misses or, more precisely, that resultant of force, all the gravitational forces is equal to zero. Using of the actual law of gravitation it has appeared that the closer point is to a shell the stronger it is attracted to it. Dierently, any spontaneous obturating of a material medium of the Universe as a shell conducts to the further shaping of such shell. That is why the Universe has cellular structure in major gauges where the aggregations of galaxies are in thin walls of these meshes and superaggregation and on crosses of meshes.

It is necessary to note, that in 1971 Karlsson has found out for the rst time a cyclic change of a spectral radiant density of quasars proportional argument ln (1 + z), where z is red bias of their spectrums. Such allocation of quasars correlates with allocation of galaxies forming in the Universe homogeneous thin-walled aggregations as meshes.

In view of the formula (II.18) cyclic changes of a spectral radiant density of quasars are conversed to cyclic dependence of allocation of quasars on distances indicating homogeneity of the Universe not only in space, but also in time, that is on its stationarity for the last a minimum of 40 billions years (so much time the electromagnetic waves went to us from the farthest quasars).

Thus, the author has designed the new stationary model of the Universe which approximately on 40 parameters is compounded with the properties of the actual Universe and has the same right on existence as well as model of Big Bang.

Quasars and the Large-scale Structure of the Universe

207

Appendix III

THE FIRST DEDUCTION OF THE PROPAGATION LAW OF LIGHT

From the regularities of the interaction of moving objects with the substance of the Universe, which have been considered in Appendix II, the conclusion is drawn that the gravitational potential should permanently act on a moving photon, i.e., quantum of light. Let us determine the said potential

0=

GM0 R0

=

G4R300 3R0

=

=

R0

=

r
c

3 4G0



=

c2:

4G0R20 3

=

(III.1)

The result obtained is evidence of a lack of innite gravitational potentials in a homogeneous and isotropic space. It is in this way that a so-called gravitation paradox is solved. This is rst. Second, the photon, when propagating in the space should lose its energy. In fact, the acceleration of gravity on the surface of the range of gravitational interaction is determined by expression

g0 = Hc;

(III.2)

in which abbreviation

H

=

r

4G0 3

:

(III.3)

is introduced. Then, taking into consideration expressions for the
energy

E = h;  E = mc2;

(III.4)

which determine the equivalent mass of a photon

m

=

h c2

;

(III.5)

and the energy conservation law, we can write the equality

h

=

h c2

g0dr

+

h 0 ;

(III.6)

where ; 0 are frequencies of light before and after the light has passed the distance dr. Planck's constant cancels out the expression. Then allowing that  0 = d , we get the equation

d dr

+

H c



=

0:

(III.7)

Having regard to the relation c=H = R0 , we nally obtain

d dr

+

1 R0



=

0:

(III.8)

Thereby, we have derived the law of propagation of light for the Universe. It can also be expressed in an integral form, if we integrate equation (III.8),

r

 = 0 e R0 :

(III.9)

As a rst approximation expression (III.9) becomes


 = 0 1

r R0

(III.10)

or in other presentation



0 0

=

H c

r:

(III.11)

Considering the Doppler eect for the source and the receiver of light, which move away one from the

other



0 0

=

v c

;

(III.12)

(it will be clear later why we use such a presentation), we come to dependency

v = H r:

(III.13)

This is just the Hubble law. Thus in the linear approximation the law of propagation of light can be easily confused the Doppler eect. This was the case when the redshift in the radiation spectra of outlying galaxies was interpreted as the galaxies bouncing apart, i.e., the universal extension of the Universe. It was no wonder (though also revolutionary), as the Doppler eect had been studied very well and the properties of the Universe as a nonconservative system did not follow from anywhere. Note that the general relativity in its conventional formulation rules out this property of the nonconservative Universe.
The law of propagation of light (III.9) is yet more evidence that the Universe does not expand at all and that the light, when spreading in the space, loses its energy since the light is permanently forced to break away from gravitating masses behind.
The numerical value of Hubble's constant is approximately equal to 1.67 10 18 s 1 , which corresponds to the equivalent speed of 51.6 km/s Mps of the extension of the Universe.
Presently, the redshift in the spectra of galaxies serves as an instrument to calculate the distance to the galaxies. For this purpose the variable z is used which is expressed via the wavelength of light

z

=



0 0

;

(III.14)

208

N.A. Zhuck, V.V. Moroz, A.M. Varaksin

Figure III.1: Diagrams of distances to galaxies and quasars

and the calculated formula [55]

r1

=

(1 (1

+ +

z)2 z)2

+

1 1

c H

:

(III.15)

If we utilize the deduced law of propagation of light (III.9), we reveal that the calculated formula should be quite dierent

r = R0 ln (1 + z) :

(III.16)

In Fig. III.1 diagrams of distances to galaxies are presented: the dash curve r1 corresponds to calculations by formula (III.15); the solid curve r corresponds to calculations by formula (III.16); the dotted curve er shows the dispersal of errors if one uses formula (III.15). (When drawing the diagrams, we set R0 = c=H = 1).
It is easy to see from this gure, that when determining the distance to a galaxy by the conventional method, errors become conspicuous starting from z = 1. When z arrives at 5...6 the value of the error reaches the magnitude of the measurable parameter itself, i.e., the distance. This leads to errors in the description of the general pattern of the world, though the premises to doubts the correctness of formula (III.15) have existed for a long time.

Appendix IV

THE SECOND DEDUCTION OF THE PROPAGATION LAW OF LIGHT

The unrestricted motion equation of material body in the line of arbitrary coordinate X for free cosmic space (ether) is represented in Appendix II

d2X dt2

+

H

dX dt

=

0;

(IV.1)

where H is the Hubble constant, which evaluate

through the gravitation constant G and the average

density of the Universe 0 by formula

H

=

r 4G0 3

:

(IV.2)

The equation (IV.1) shows that the ether has vis-

cosity. Also it was shown that the bearer both gravita-

tional, and electromagnetic interactions is the medium

(ether) consisting of particles (amer)  by a mass about 10 69 kg.

Considering, that the equation (IV.1) is valid for

material body of any nature we apply it for description

of motion these particles. On the other hand, taking in-

to account a polarizability of an ether, i.e. the presence

in it of elastic properties (that is been conrmed by

spread of wavelike processes as electromagnetic waves)

iintetmheo!b02tXainendameqeudattihoen

it is necessary recovery force

to add (here

one more !0 is the

ether particles oscillations eigenfrequency). As a result

the motion equation will be obtained



d2X dt2

+

H

dX dt

+

!02X

=

0;

(IV.3)

where X is a shift of ether particle at any moment of time.
As the mass of ether particle is been a member of all items of the obtained equation then it is possible to exclude its and to simplify the equation to a view

d2X dt2

+

H

dX dt

+

!02X

=

0:

(IV.4)

The equation (IV.4) is a desired equation of ether particles motion. We shall search its solution in the form of

t X = e 2 cos (!t + ') ;

(IV.5)

where  , ! and ' are unknown quantities. By direct substitution is determined that (IV.5) is a solution of the equation (IV.4) for any ' provided that



=

1 H

;

(IV.6)

!2 = !02

H2 4

:

(IV.7)

The most common solution of the equation (IV.4)

is a superposition of two linearly independent solutions

with two initial conditions for shift

velocity t = 0.

F(doXr =exdat)m0 p=le,X_w(e0)sh=alXl_ t0akoef

X (0) = X0 and ether particles by ' = 0 and ' =

=2. Then common solution of the indicated equation

is possible to present as

Ht X = e 2 (C1 sin !t + C2 cos !t) ;

(IV.8)

Quasars and the Large-scale Structure of the Universe

209

where C1 and C2 are integration constants. For their denition at rst we shall determine derivative of expression (IV.8)

dX dt

=

e

Ht 2 (C1! cos !t

C2! sin !t)

H 2

e

Ht 2 (C1 sin !t + C2 cos !t) :

(IV.9)

At t = 0 from (IV.9) and (IV.8) we shall have

C1

=

1 !


X_ 0

+

H 2


X0

;

(IV.10)

C2 = X0:

(IV.11)

and that ct = r is a distance into which the oscillatory process in space can be spread, we obtain familiar from a cosmology dependence for decrease of frequency of electromagnetic waves with distance

r

 = 0 e R0 :

(IV.19)

On a basis (IV.19) an expression for denition of distances up to far space objects (galaxies and quasars) is obtained

r = R0 ln (1 + z) ;

(IV.20)

where

z

=



0 0

(IV.21)

After that the expression (IV.8) becomes [1]

is a redshift of their radiation spectrums.

X= e

Ht 2



1 !


X_ 0

+

H 2


X0

sin

!t

+

X0

cos


!t

:(IV.12)

The law (IV.19) have been completely proved by observations [28]:
| by real presence of redshift in radiation spectrums of galaxies and quasars;

10

F18or sfee1blies

attenuation (and it is real so, as negligible quantity) exponential

H
factor

exp ( Ht=2) is possible to consider as stationary value

during one cycle of oscillations. Under such conditions

it is possible to neglect an augend in (IV.9) and easily

to show, that the total energy of a particle E (the sum

both kinetic and potential) is equal

| by the missing of bright luminescence of the sky at night (contrary to a known photometer paradox of classical physics);
| by presence of microwave background radiation of space which is aggregate radiation of all stars of the Universe with taking into account the law (IV.19);
| by Hubble diagram which in a linear part coincides with the diagram obtained on the basis of the law

E

=

X_ 2 2

+

!02X2 2

= E0 e

Ht;

(IV.13)

where the initial value of particle energy E0 is deter-

(IV.19); | by allocation of galaxies and quasars in space of
the Universe (this discovery is still developed).

mined by expression

E0

=

 4

!2 + !02

C12 + C22 :

(IV.14)

As in a microworld there is a quantization of energy proportionally by Plank constant h, the energies E and E0 will be proportional to frequencies  and 0 by the formulas

References [1] Crowford F. \The Berkeley course of physics. V. 3.
Waves." McGraw-Hill Book Co., 1968. [2] Einstein A. \Die Feldgleichungen ger Gravitation.
Sitzungsber. preuss. Akad. Wiss., 48, 2, 844{847 (1915). [3] Einstein A. \Die Grundlage ger allgemeinen Relativ-

E = h; E0 = h0:

(IV.15) (IV.16)

itatstheorie. Ann. Phys., 49, 769{822 (1916). [4] Friedmann A. \Uber die Krummung des Raumes."
Ztschr. Phys., 10, 377{386 (1922).

Then from expression (IV.13) we have dependence for decrease of particle oscillation frequency in the time

 = 0 e Ht:

(IV.17)

Being aware of Ref. [28] that the Hubble constant H is bound to radius of gravitational interactions R0 by dependence (c is velocity of light)

H

=

c R0

;

R0

=

r
c

3 4G0

;

(IV.18)

[5] Friedmann A. Ztschr. Phys., 21, 336{332 (1922). [6] Gamov G. Phys. Rev., 70, 572{573 (1946).
[7] Grishchuk L.P., Petrov A.N., Popova A.D. \Exact Theory of the (Einstein) Gravitational Field in an Arbitrary Backgraund Space-Time." Comm. Math. Phys., 94, 379{395 (1984).
[8] Hubble E. \A relation between distance and radial velocity among extra-galactic nebulae." Proc. NAS, 15, 168 (1929).
[9] Karlsson K.G. \Possible discretization of quasar redshift," Astron. and Astrophys., 13, 333, (1971).

210

N.A. Zhuck, V.V. Moroz, A.M. Varaksin

[10] Khodjachich M.F. \Csmological periodicities in radiospectrums of quasars," Spacetime & Substance, 1, 3, 120 (2000) (in Russian).
[11] Kontorovich V.M., Krivitsky D.S., Kats A.V. \Explosive"evolution of galaxies (an analog of collaps) and appearance of quasars in the merger model." Physica D 87, 290 (1995).
[12] Logunov A.A., Mestvirishvili M.A. Progr. Theor. Phys. 74, 31{50 (1985).
[13] Logunov A.A., Mestvirishvili M.A. Sov. Particles and Nucleas. 17, 1{153 (1986).
[14] Logunov A.A., Mestvirishvili M.A. \The Relativistic Theory of gravitation." Moskow, Nauka, 1989, 304 pp. (in Russian).
[15] Mach E. \Die Mechanik in Ihrer Entwicklung, Historisch-Kritisch Dargestellt." Leipzig: Brokhaus, 1883.
[16] Penzias A.A., Wilson R.W. Astrophys. J., 142, 419{ 427 (1965).
[17] Shaver P.A. \High Redshift Quasars." Seventeenth Texas Symposium on Relativistic Astrophysics and Cocmolody. Annals of the New York Academy of Sciences, 759, 87 (1995).
[18] Zhuck N.A. \On the some results following from the universal gravity law." Borisoglebsk, 1986, 58 pp. (in Russian).
[19] Zhuck N.A. \Metamorphoses of cosmology." In \The Relativity Theory: for and against," FENID, Gomel, 3, 89 (1991) (in Russian).
[20] Zhuck N.A. \The cosmological solutions of the Einstein equations." Kharkiv, KhVVAUL, 1995, 16 pp. (in Russian).
[21] Zhuck N.A. \New overviews about the Universe and its laws." The 1-st RTI TTR scientic conference, RTI TTR, Kharkiv, 1998, 5{14 (in Russian).
[22] Zhuck N.A. \The cosmological solutions of the Einstein equations," Kyv, Author's Certicate of series PA, No 1718 with a priority of January 28, 1999 (in Russian).
[23] Zhuck N.A. \The new stationary model of the Universe." The Gamov memorial international conference \The Univerce of Gamov: original ideas in astrophysics and cosmology" (GMIC'99), Odessa, August 16{22, 1999, Abstracs, p. 37.
[24] Zhuck N.A. \Cosmic equilibrium electromagnetic radiation," Kharkiv Univ. Public., 456/2, 2000, p. 244 (in Russian).
[25] Zhuck N.A. \The Microwave Background Radiation as aggregate radiation of all stars." The XVII international conference \Actual problems of extragalactic astronomy," Puschino, Moscow region, Russia, April 12{14, 2000 (in Russian).
[26] Zhuck N.A. \The axiomatic theory of the Microwave Background Radiation." The Joint European and National Astronomical Meeting \European Astronomy at the Turn of the Millennium" (JENAM-2000), Moskow, Russia, May 29 { June 3, 2000, Abstracs, p. 48.

[27] Zhuck N.A. \About identity of inertial and gravitational masses." The Joint European and National Astronomical Meeting \European Astronomy at the Turn of the Millennium" (JENAM-2000), Moskow, Russia, May 29 { June 3, 2000, Abstracs, p. 168.
[28] Zhuck N.A. \Cosmology," Kharkiv, Model Vselennoy Ltd, 2000, 464 pp. (in Russian).
[29] Zhuck N.A. \Field formulation of the General Relativity and cosmology." The Ukrainian-Russian conference \Gravitation, cosmology and relativistic astrophysics" (GRAV{2000), Kharkiv, Ukraine, November 8{11, 2000, Abstracs, p. 37.
[30] Zhuck N.A. \Cosmological eects in bulky MichelsonMorley interferometers." The Ukrainian-Russian conference \Gravitation, cosmology and relativistic astrophysics" (GRAV{2000), Kharkiv, Ukraine, November 8{11, 2000, Abstracts, p. 73.
[31] Zhuck N.A. \The identity of inertial and gravitational masses is proved!" Spacetime & Substance, 1, 1, 23{28 (2000). http://spacetime.narod.ru.
[32] Zhuck N.A. \The Microwave Background Radiation as aggregate radiation of all stars." Spacetime & Substance, 1, 1, 29{34 (2000). http://spacetime.narod.ru.
[33] Zhuck N.A. \Gravitation viscosity and geotetic curvature of the Universe." Spacetime & Substance, 1, 2, 71{ 77 (2000). http://spacetime.narod.ru.
[34] Zhuck N.A. \Gravitation viscosity and geotetic curvature of the Universe." Spacetime & Substance, 1, 3, 1{5 (2000). http://spacetime.narod.ru (in Russian).
[35] Zhuck N.A. \Field formulation of the General Relativity and cosmology." Spacetime & Substance, 1, 4, 71{77 (2000). http://spacetime.narod.ru.
[36] Zhuck N.A. \Cosmological eects in bulky MichelsonMorley interferometers." Spacetime & Substance, 1, 5, 71{77 (2000). http://spacetime.narod.ru (in Russian).
[37] Zhuck N.A. \Field formulation of the General Relativity and problems of cosmology." Spacetime & Substance, 2, 1, 71{77 (2001). http://spacetime.narod.ru.
[38] Zhuck N.A. \The Cosmos Microwave Background Radiation as aggregate radiation of all stars." Physics of Consciousness and Life, Cosmology and Astrophysics, 1, (2001). (In Russian).
[39] Zhuck N.A. \Properties of the Yukawa potential and gravitational screening of a substance." Spacetime & Substance, 2, 3, 105 (2001). http://spacetime.narod.ru.
[40] Zhuck N.A. \On the united nature of gravitational, electromagnetic and nuclear interactions." Spacetime & Substance, 2, 4, 165 (2001). http://spacetime.narod.ru.
[41] Database on quasars (the basis is taken as of June 29, 2001). http://cdsweb.u-strasbg.fr/cgi-bin/cat?VII/215.
[42] N.A. Zhuck, V.V. Moroz, A.M. Varaksin, \Quasars allocation in the Universe." Homepage, http://quazars.narod.ru.


Spacetime & Substance, Vol. 2 (2001), No. 5 (10), pp. 211{225
c 2001 Research and Technological Institute of Transcription, Translation and Replication, JSC

ETHERAL WIND IN EXPERIENCE OF MILLIMETRIC
RADIOWAVES PROPAGATION
Yu.M. Galaev1
The Institute of Radiophysics and Electronics of NSA in Ukraine, 12 Ac. Proskury St., Kharkov, 61085 Ukraine

Received August 26, 2001

The phase method of anisotropic media parameters measurement of electromagnetic waves propagation is proposed. The experimental hypothesis check about the existence of such material medium of a radiowaves propagation in the nature, as Aether is executed in eight millimeter radiowaves range. The ethereal wind speed and this speed vertical gradient near the Eath's surface have been measured. The systematic measurement results do not contradict the initial hypothesis rules and can be considered, as experimental imagination conrmation about the Aether existence, as material medium, in the nature.

1. Introduction
The experimental researches of the ground channel phase characteristic of 8-mm range radiowaves propagation have revealed the problems, connected with its model elaboration [1{4]. The model [3] described the possible spatial eects in
uence, but this idea has not been developed further due to the quantitative divergence between demanded and measured atmosphere parameters. The interference model [4], as a whole, explained the observed eects, but in some cases the qualitative divergence between the calculation and measurement results took place. The further problem analysis has shown that the hypothesis engaging of the radiowaves propagation medium anisotropy has enabled to give the calculation results in conformity with the measurement results. It was supposed that the anisotropy is stipulated by the directional medium motion of radiowaves propagation and this medium 
ow has the space origin. Some information about such medium motion parameters was taken from the papers [5{7]. The works [5, 6] have been executed in order to the hypothesis experimental check about the Aether existence in the nature as the material medium, which lls the Global space and is the building stu of all kinds of matter, the motions of which are revealed like physical elds and interactions. In due course the positive work results [5] were widely known, but they have been estimated by scientic community, as error because of some reasons. The hypothesis about the existence of such material medium, as Aether, in the nature wasn't accepted. We'll consider the major work results, which were executed in this direction tak-
1e-mail: galaev@ire.kharkov.ua; Ph.: +38 (0572) 448742

ing into consideration the long-life and signicance of the problem. We'll try to determine the reasons, which have made the physicists of that time consider the work results [5, 6] as error and refuse the Aether concept.
In 1877 D.K. Maxwell noticed, that while the Earth motion through Aether there should be an ethereal wind on the surface, which changes the light speed distributing in Aether. It is known that A.A. Michelson tried to nd out an ethereal wind in 1881 for the rst time [8, 7]. With the help of a cross shaped interferometer with the length of the optical path about 2.4 m, within the hypothesis of xed Aether, he expected to receive the bands displacement of an interference pattern, conforming the orbital motion speed of the Earth by the value 30 km/s. However the measured displacement, which corresponded the speed by the value only 3{4 km/s. Michelson related this result to measurement errors and concluded about the initial hypothesis inaccuracy of stationary Aether. However, it is considered in physics almost since that time, that \Michelson experience" has shown in general the inaccuracy imagination about such medium existence as Aether in the nature. Many explorers didn't agree with such matters. The attempts to nd out this medium continued, including Michelson himself.
In 1925 D.K. Miller received the optical path of the length about 64 m with a cross-shaped interferometer, as a result of long systematic measurements, that the suspected ethereal wind speed at the altitude 265 m above the sea level (Clevelend) has the value about 3 km/s, and at the altitude 1830 m (observatory Mount Wilson, Pasadena) is about 10 km/s. The motion apex coordinates of the Solar system were determined: the direct ascension 17:5h , declination +650 [5].

212

Yu.M. Galaev

The Miller works have attracted the great physicists' attention. The discussion has started about them, in which the in
uence of possible unaccounted factors on an optical interferometer was discussed rst of all. In the work [10] S.I. Vavilov expressed, perhaps, the common opinion formed: \...the Miller's interferometer is so sensitive, that many local in
uences, considered hard, can be the cause of systematic bands displacement". Here again: \In any case, the experiments repetition in the other place and by the other device is necessary at this situation." It was clear, that the interferometer is required to save the environment parameters from the change aect. The solution seemed apparent the interferometer should be placed into the thermostat and then into the pressurized chamber together with the thermostat. So it happened, but all the attempts in order to repeat Miller's experiment, except the experiment [11], were performed by the devices, which were placed in metallic chambers. R.D. Kenedy [12, 7] increased the interferometer sensitivity. The device was placed in the pressurized metallic chamber. The measurements were conducted at the same altitudes, as in [5]. The bands displacement was not observed. K.K. Illingwort [13, 7] improved Kennedy's device, but also these measurements showed a zero result. E. Stael [14, 7] placed an interferometer in the metallic chamber, i.e. thermostat, and raised it in an air balloon up to the altitude 2500 m. The required eect was not observed. In 1929 the work by A.A. Michelson, F.G. Peas, F. Pirson appeared [11]. In this experiment, at the same observatory Mount Wilson, the bands displacement of an interference pattern value no more than 1/50 of the expected eect was measured with the interferometer having the optical path length about 26 m, connected with the solar System motion having the speed 300 km/s. In other words, the speed of relative motion of the value 6 km/s was measured. The interferometer has been placed into a fundamental building of the observatory optical workshop for work temperature regime stabilization. The pressurized metallic chamber was not applied. Unfortunately, the problems, which the authors overcame at the experiment execution, were listed in general in this extremely laconic work (1 page). The measured results are presented only in such kind as they were given in the above mentioned work.
The experiment by G. Yoosa 1930 [15] was the last experiment on the ethereal wind detection, which was executed with an optical interferometer. The device was made on the quartz basis by the corporation Tseys, it was hanged in the vacuum-metallic chamber and supplied with photographic registration. The measurement results showed that the required ethereal wind, in any case, does not exceed the value 1 km/s (the device resolving capacity). Miller's measurements should be considered nally as the error ones and stipulated by outside causes after zero work result [15].
In 1933, Miller has marked the shielding property

of metal covers in his work [6]. However the scientic community did not react properly to such peculiarity, shown by him in this work, as, perhaps, the positive work results [11], as there was a lot of experiments with zero results obtained with the interferometers, screened by metallic chambers by that time. The physical shielding phenomenon interpretation was given by V.A. Atsukovsky [16] for the rst time, having explained it by the fact, that the electrons in metals will create socalled \Fermi's surface".
After 1930 Michelson-Miller's experiment ceased to take a central place in physics. Only in 50 years, there was a capability of the experiment realization, which didn't repeat Michelson's scheme, but being its analogues in the results interpretation sense after the devices appearance, based on completely other ideas (resonators, masers, Mossbauer eect etc.). Such experiments were conducted [17{20]. And again, the common tool error of these experiments was the usage of ethereal wind eects detection of dierent metallic chambers. They were metallic resonators in [17, 18, 20], lead chamber in [19], since it was necessary to work with a gamma-radiation. The works' authors, perhaps, have not given the proper signicance to Miller's conclusions 1933 [6] about the inapplicability of metal boxes in the experiments with an ethereal wind.
Thus, proper checks of Miller's experiments weren't conducted yet until nowadays, in spite of numerous physicists' attempts to repeat his experiments! All his followers carefully screened the devices from an ethereal wind by metal chambers, and, according to A.A.Atsukovsky's image expression, \...it's the same that to make the attempts to measure the wind, which blows outdoors, looking on the anemometer put in a densely close room" ([7], p. 4). The known works until nowadays cannot be ranked as experiments, which could conrm or deny Miller's results, conrm or deny the hypothesis about Aether existence in the nature. The measuring means, unsuitable for ethereal wind eects measurement, were applied in all these works.
The great job for work collecting and analysis, dedicated the ethereal wind problem, was performed by Atsukovsky [7]. The aether model is oered and the aether dynamic picture of the world was designed in his works [21, 22, 16]. The Aether is represented as a material medium, which lls in the global space and has the properties of viscous and compressible gas, it is a building stu for all material formations. The element of Aether is an amer. The physical elds represent dierent forms of Aether motion, i.e. the Aether is a material medium of electromagnetic waves propagation. The gradient boundary layer is formed at mutual motion of the Solar System and Aether near the Earth surface, in which the Aether running speed (ethereal wind) increases with an altitude. The ethereal wind apex is northern. It is shown, that the metals have larger aether dynamic resistance and interfere the Aether

Etheral wind in experience of millimetric radiowaves propagation

213


ows. Therefore metering devices arrangement in metal chambers is inadmissible. The reason of failures is due to it [12{14 etc.]. The work authors [7, 16, 21, 22] consider that the experiments [5, 11] are authentic.
However the positive work results [5, 11] couldn't be considered as nal experiment currently, after which the doubts regarding the denite physical concept are removed. The matter is that within modern imagination about the light speed constancy, the fact nding of the Earth and Solar system motion in space availability is not enough to make a conclusion about Aether existence, as material medium, i.e. medium consisting of separate particles. So, Sanyak's known rotary effect and the relative movement, discovered with it, for example the Earth's diurnal rotation [23, 7], in modern physics is interpreted without engaging the Aether hypothesis existence [24]. Essentially, the attempt to show that the discovered motion is conditioned by the Earth relative movement and Aether material medium were made by two explorers: Miller [5] and Staal [14], but both made the essential methodical errors. Miller placed the interferometer at dierent altitudes and obtained that the speed of the discovered motion raised with the altitude increase over the Earth's surface. There shouldn't be such relation in case of movement in space, without Aether availability, as the material medium 
ow. However these major measurements, executed in [5], are methodically incorrect: the measurements are carried at dierent altitudes in time; the measurements are conducted in the environment various conditions (temperature, humidity, pressure, solar radiation, air
ows, etc.), the interferometer is rather sensitive to the environment parameters variability; the measurements, strictly speaking, are conducted by miscellaneous devices, since Miller's huge interferometer was disassembled, assembled again and adjusted while moving from Clevelend to Mount Wilson observatory. Therefore, the technique, which Miller applied for speed dependence measurement of the discovered motion from an altitude above the Earth's surface, was unacceptable to make a nal conclusion for the benet of Aether existence, as material medium. Staal tried to apply more correct technique for this problem solution [14]. The optical interferometer mounted on an air balloon, rose up to the altitude 2500 m. The interferometer was placed into the pressurized metal chamber (the thermostat) for stabilization of the working conditions. As it has already been emphasized, the application of metal chambers is completely inadmissible at such measurements. This circumstance was not known at that time. It occurred, that the measured displacement of interference bands corresponds to the ethereal wind speed of 7 km/s with the error of the same magnitude order. The conclusion of the author's work [14]: \We can not discuss Miller's result on the basis of this experimental series, as our measurements accuracy is just on the border of Miller's observations. However we can ex-

clude Miller's eect, raised with the altitude increase." In other words, the motion could be nd out, and highaltitude relation of this speed misses completely.
Thus, considering the work lacks [5, 11] and large number experiments availability with zero result, it is possible to understand the physicists disbelieving to the works at that time [5, 11], the results of which indicated the necessity of the fundamental physical concepts change.
Positive results of the data application [5, 6], at the experiments analysis [1-4], detected reasons of unsuccessful attempts to repeat Miller's experiments, showed, that it is necessary to make the experiment again in order of the hypothesis check of the electromagnetic waves propagation material medium | Aether existence in the nature. It is necessary to solve the following problems for this purpose. It is necessary to take into account the lacks, allowed in earlier conducted researches; to apply other measurement methods, which will enable to show the Earth's relative movement availability in the unied measurement act in a single experiment and that the motion is stipulated by the Earth relative movement and the material medium 
ow of electromagnetic waves propagation and this medium motion has a space parentage. The positive result of such experiment can be considered as the experiment hypothesis conrmation of Aether material medium existence in the nature.
2. Measurement method
The Aether model has been adopted as the initial hypothesis and oered in the works [21, 22, 16] while the experiment accomplishment. The following eects should be observed in this case at electromagnetic waves propagation near the Earth's surface. The anisotropy eect, i.e. wave propagation velocity depends on the radiation direction that is stipulated by the Earth and Aether relative movement, i.e. the medium of electromagnetic waves propagation. The altitude eect, i.e. the wave propagation velocity depends on the altitude above the Earth's surface that is stipulated by Aether viscosity, i.e. the material medium of electromagnetic waves propagation. The space eect, i.e. the wave propagation velocity along the Earth surface changes the value within one day, that is stipulated by the space origin of ethereal wind. Thus as a result of the Earth's diurnal rotation the altitude (astronomical coordinate) of the Solar System motion apex will change its value within sidereal dayowing as for any other aster. Therefore horizontal component of ethereal wind speed and, therefore, the rate of electromagnetic waves propagation along the Earth's surface will change their values within the same term. Therefore, according to the research problems, the measurement method should be responsive to the indicated eects, and provide their

214

Yu.M. Galaev

Figure 1: The experience scheme
observation in the unied measurement action. The method of measurement is applied in the work,
based on the reciprocity principle rules in electrodynamics [25], according to which the radiowaves propagation conditions from one point of a radio link to the other are completely those, as well as backwards and this symmetry does not depend on the interspace properties, which is only supposed to be isotropic. If the radiowaves propagation velocity depends on the radiation direction, such space is anisotropic and the reciprocity principle is not applied. The ground radio link of a line-of-sight with a counter radiowaves propagation of a millimeter-wave is used at the method implementation. In this case the main elds formation mechanizm in the acceptance points is the interference of direct waves and waves, re
ected from the Earth's surface, i.e. waves, which spread at miscellaneous altitudes from ground [26]. It enables, comparing the wave interference results to nd out the development of anisotropic and altitude eects simultaneously in both points. The space eect was found out, as well as in [5, 6], by the results averaging of systematic measurements executed to scale the sidereal time S.
Let's consider the operational principle of the measurement method. The experience scheme is shown in the Fig. 1
The letters A and B indicate the transceiver points of the radio link. Two waves come there at each of these points: a straight line distributing on a pathway AB at the altitude Zup above the Earth's surface, and the wave, re
ected from the Earth's surface in the point C . The expansion of a pathway AB is r. The medium trajectory height ACB is Zl . The arrows indicated as Wrup and Wrl , demonstrate the radial component direction of the ethereal wind speed, i.e. the component, which is operational along the radio link. Their lengths are proportional to ethereal wind speeds at the altitudes Zup and Zl . The radio link represents the

radio interferometer, which due to the Earth's diurnal rotation turns into the Aether 
ow. The characteristics measurement method of the radio tracts is applied for observation of the wave interference [27]. The method essence is in the following. The zonding modulation signal I with a carrier frequency f0 and the frequencies lower (f1 = f0 F ) and upper (f1 = f0 + F) of the lateral components (F is a modulating frequency) emits from the transmitting point. At propagation each i signal component I receives the phase increment 'i (the indexes i = 1; 2 correspond to the frequencies f0;1;2). The adopted signal component with the frequency f0 is multiplied separately from each of lateral components in the receiving device, and the phase shift 'i is measured between the multiplication results having dierential frequencies. The expression for
'i looks like

' = (' 0 '1) ('2 '0)

(1)

Such phases combination is invariant to the time zero change and received the name \a phase invariant" in the paper [28]. Let's nd the value 'i at a wave interference in the radio link points, shown in the Fig. 1. In this case, the resultant oscillation phase with i frequency can be determined with the following known expression [29]

'i

=

kir

+

arctg

1

R sin (ki + R cos (ki

r

+ r

) +

);

(2)

where: ki = 2=i is the wave number; i = c=fi is the wavelength; c is the radiowave propagation velocity in the xed Aether (W = 0), in vacuum; R is the module of the re
ection coecient; is the phase of the re
ection coecient; r is the propagation dierence between direct and re
ected waves. As in the experi-
ment Zup  r, it is possible to consider, that  
[29]. Then (2) will be like

'i = kir + arctg 1

R sin (ki R cos (ki

r) r)

:

(3)

Let's designate

Mi = arctg 1

R sin (ki r) R cos (ki r)

(4)

Let's record (3) as 'i = ki + Mi and we shall substitute 'i into (1). Allowing, that
k2;1 = k0 k; k = k0 k1 = k2 k0; we shall receive

' = (M0 M1) ( M2 M0) :

(5)

We'll decompose (4) into Taylor rows in the point neighborhood k0 r according to the powers ( k r). Limiting by the rst four decomposing members, we shall record:

M1 = M0

k

rM00 +

1 2

k2

r2M000

Etheral wind in experience of millimetric radiowaves propagation

215

1 6

k3

r3M0000 +

;

(6)

M2 = M0 +

k

rM00

+

1 2

k2

r2M000 +

+

1 6

k3

r3M0000 +

(7)

Let's substitute the values M1 , M2 , dened by the expressions (6), (7), into (5), we shall obtain

' = ( k r)2 M000:

(8)

Let's calculate the second derivative M000, then (8) will be like

'=

(

k

r)2

R (1 +

1 R2

R2 sin k0 2R cos k0

r r)2

:

(9)

The expression (9) introduces the phase invariant value ' in an interference case in the reception method point of direct waves and the waves, re
ected from the Earth's surface distributing on the pathways AB and ACB . For problem solving of the research results of simultaneous values measurements 'A and
'B , in the points A and B accordingly, we shall deduct one of the other

= 'A 'B

(10)

In the considered method is the measured value. According to the reciprocity principle, at the radiowaves propagation in the isotropic medium 'A =
'B . In this case = 0: In case of the anisotropic medium the reci-
procity principle is not applied and 6= 0.
It follows from (9), that at xed values k and k0the value ' depends on R and r. In the paper the data about actual values R, i.e. having a place in a radio link, selected for measurements, are obtained experimentally at this radio link characteristics analysis. The information about the value R change range can be found, for example, in the paper [26]. The propagation dierence r is determined by the radio link geometry, but at the radiowaves propagation in atmosphere, owing to radiowaves refraction, as well the value r depends upon the gradient value gn of the high-altitude prole of the atmosphere interception factor n (Z) [29]. At the linear (and close to it) relation n (Z) the value gn in the atmospheric layer Z = Zup Zl can be determined as

gn = (nup nl) = Z;

(11)

where nup; nl is the index coecient of air at heights Zup; Zl .
The direct wave propagation velocity is (Wup = Wl = 0) the velocity of propagation of a direct wave is equal Vup = c=nup , the wave velocity, re
ected from

the Earth's Then (11),

surface is Vl = c=nl taking into account,

tihnatthVeuipsVoltropicc2

case. , can

be written like

gn = (Vl Vup) =c Z:

(12)

In the anisotropic case (Wup > Wl > 0, that corresponds the positions of an initial hypothesis) the radiowave propagation velocity is V and its relation to the altitude V (Z) depend on the radiation direction, that is stipulated by the gradient medium 
ow of radiowaves propagation, i.e. Aether (Fig. 1) available. In this case wave propagation velocities at altitudes Zup and Zl are

Vup

=

c nup

Wrup;

Vl

=

c nl

Wrl;

(13)

where the sign \+" is applied, when the radiowaves propagation direction coincides the ethereal wind direction, and the sign \-" is applied, when these directions are inverse. Let's put the values Zup and Zl in (12). If the propagation directions of radiowaves and ethereal wind coincide, we shall receive

gn+

=

c

1 Z

c nl

+

Wrl

c nup


Wrup :

(14)

Let's open brackets, then

gn+

=

nup nl Znlnup

Wrup c

Wrl Z

:

(15)

Allowing, that nlnup  1, (nup nl) = Z = gn,
and (Wrup Wrl) = Z = gWr is the gradient of the ethereal wind speed radial component in the layer Z , the expression (15) can be written as

gn+  gn gWr=c

(16)

The rst sum member (16) represents the highaltitude prole gradient of the atmosphere refraction coecient gn in the layer Z . The second member represents the additional component to gn, stipulated by the velocity gradient availability in the ethereal wind 
ow gWr . At the radiowaves propagation towards the ethereal wind motion, it is possible to receive

gn  gn + gWr=c

(17)

It follows from (16), (17) that if the Aether gradient 
ow is available, the wave refraction distributing in counter directions, will be dierent by virtue of
gn+ 6= gn .
Let's consider the oered measurement method action with reference to a concrete experimental radiolink, taking into account the features of hardware implementation of this method now. Let's estimate the values of probable hardware and methodical measurement errors.

216

Yu.M. Galaev

Figure 2: The experimental radiolink prole

Figure 3: The high-altitude eld prole

3. Experimental radiolink

The measurements are conducted with the ground radiolink of direct visibility within 13 km. The radiolink prole is shown in the Fig. 2.

The points A and B are the nal transceiver points

in the gure. The point A was on the northern side

of Kharkov, the point B was in the village Russian

Tishky. The aerial of the point A was at the altitude 30

m from the Earth's surface, and the aerial of the point

B was at the altitude 12 m. The hill top D, the terrain

in the region of the point C and point B have the grass

covering. The hill top E is occupied with forests. The

medium trajectory height is AB overland Zup  42 m.

The lumen value above the top D, denited by geodesic

mA eutphotdo,tihse Hto1pD2r51:3 m22.0T0 mhe.

interval from The azimuth

the of a

point radio

link, measured in the point A regarding the meridian,
  450. To specify the elds formation mechanizm

in radiolink points, the vertical eld structure is mea-

sured in the point A. The measurements are executed

in summer, in August. The radiation was conducted by

the aerial of the point B on a carrier frequency of this

point zonding signal. The vertical probing is execut-

ed by consequent rise of the auxiliary receiving device

saugprapmlie(dw1it0h0

the aerial of rather broad ). The rise started from a

directional diaerial arrange-

ment level of the point A. The measurement results are

shown by the points on the left-hand piece of the Fig. 3.

The continuous line approximates the view of measured eld structure. The power P of the received signal in decibels regarding the reference level P0 is plotted on an abscissa axis. The height of the auxiliary receiving device in meters is plotted on an ordinate axis.

As it is visible from the Fig. 3, the structure of a high-altitude prole contains two components mainly.

The rst structure is presented by several change terms, the second is presented only by the part of its term. The measured structure can be described by three waves

interference: the direct wave (distributing on the pathes

BA), the waves, re
ected from the top D (on the path BDA), and the waves, re
ected from the terrain in neighborhood of the point C (on the path BCA).
The problem solution of a eld calculation at several waves interference is described in the work [29]. The factor attenuation module is determined by the following formula at vertical probing

jQ

(Za)j

=

8><2
41
>:

+

X J j=1

Rj

cos


j

(Za

32 )5 +

+

2X J
4
j=1

Rj

sin


j

329>=1=2
(Za)5 >;

;

(18)

where Za is the auxiliary device uprise height; J is the interfering waves quantity; j is the wave number, re
ected from j point on the Earth's surface. The phase shift 
i (Za) between a straight line and j waves is


j (Za) = 2 1 rj (Za) + j

(19)

The propagation waves dierence at gn = 0 is

r0j

(Za)

=

[Hj + 2rqj

Hj (1

(Za)] qj)

2
;

(20)

where Hj is the lumen value above j re
ection point at gn = 0; Hj (Za) is the additional element to the value Hj , which depends upon Za ; qj = rj=r is the relative coordinate of j of the re
ection point; rj is the interval from the point A up to j re
ection point. The lumen
value at gn 6= 0 is determined by the expression

Hj (gn) = Hj 0:25r2gnqj (1 qj) :

(21)

The additional element value Hj(Za) is

Hj (Za) = (1 qj) Za:

(22)

Etheral wind in experience of millimetric radiowaves propagation

217

The calculation result is given on the right piece of

the Fig. 3, executed on the formulas (18)-(22). The fol-

lowing parameters values of re
ection points are adopt-

ed at calculations: 1;2 =  ; r1 = 2200 m; H1 = 25:3

m; R1 = value gn

0:07; r2 = 5:5

= 11000 10 8 m

m; 1.

H2 = 24 m; R2 The values R1

= 0:04; and R2

are obtained from the data of the eld vertical prob-

ing (left-hand piece of the Fig. 3). Their rather small

values (for example, in comparison with the work data

[26]) are stipulated by the following features of re
ected

waves formation in an experimental radiolink (Fig. 2).

It is: the waves divergence at re
ection from the domed

top D; the segment C was irradiated with a side lobe

of the antenna point B direction. It is visible from the

Fig. 3, that the calculation results will be agreeed with

the measurement results as a whole. The dierences

available can be explained by those that the calculation

is executed in the supposition about the independence

gn from Za .

At measurements realization, foreseen by this work

problems, the probing signals transmission in the points

A and B was implemented by the aerials with direc-
tional diagrams width  0:50. In this case the top D

was outside of the aerial chart main lobe of the point

A. Therefore the signal values, received in both points

from the top D directions, were much less (on 17...20

dB) signal values, received from the point C directions.

(As it was marked, the auxiliary aerial with the directional diagram width about 100 was applied at vertical

probing and the top D was in a main lobe of such aeri-

al). Therefore further estimations were executed within

the following supposition. The signals received in the

points A and B , represent the wave interference re-

sults, which come to these points on the pathways AB

and ACB . The following parameters of a re
ecting

segment are adopted for calculations: r2 = 11000 m; H2 = 24 m; R2 = 0:04. (As only this segment is con-

sidered below, the indexes writing is omitted and con-

sidered, that H2 = H ; R2 = R; q2 = q ; r02 = r0).

We shall substitute the value H to (20), dened by

(21) for the relation calculation r from gn , we shall

receive

r

=

2rq

H2 (1

q)

rH 4

gn

+

r3gn2 32

q

(1

q) :

(23)

The rst member (23), according to (20), represents the value r0 at gn = 0, Za = 0. The second and third members depend on gn . Thus within the change range gn , peculiar for atmosphere [30-32], the value of the third member does not exceed 0.01 from the second value. The values r0 and rH=4 are determined only in geometrical parameters of a radiolink. In this case, neglecting third member in the expression (23) and having designated rH=4 = d, we shall receive

r  r0 dgn

(24)

It follows, that anisotropic eects and altitudes result in the components occurrence to gn by value
gWr=c in an anisotropic case (Wup > Wl > 0), from (16), (17). Let's substitute values gn , dened by (16), (17) in (24). Let's receive, that the propagation dierence at propagation directions concurrence of radiowaves and ethereal wind is

r+ = r0 d (gn gWr=c) :

(25)

It is at a radiowaves propagation towards the ethereal wind motion

r = r0 d (gn + gWr=c) :

(26)

It follows, that r+ > r, r < r and r+ 6=

r from (25), (26). The dierence in these values

is determined by the velocity gradient of the ethereal

wind value gWr .

We shall estimate the possible value gWr . The es-

timations will be executed for a case, when the hori-

zontal component of the ethereal wind speed receives

the maximum value. It should be observed at the mo-

ment of the ethereal wind lower transit apex (the apex

crosses the meridian in the bottom point). In [5], the declination of the ethereal wind apex M = +650 is de-

termined in an equatorial system of astronomical coor-

dinates. The index \M" means the measurement place,

i.e. the observatory Mount Wilson. Its geographic lat-

iZtuMde'1M83=0

340 n.l., the altitude above m. In [5] the ethereal wind

the sea level speed in the

interferometer plane, i.e. horizontal component of this

speed WM , was measured, it is

WM = W cos hM;

(27)

where W is the value of the ethereal wind speed module at the altitude ZM ; hM is the apex height in a horizontal system of astronomical coordinates at the latitude 'M . Resulting in the measured data, obtained by Miller on Mount Wilson and in Clevelend, the highaltitude relation of the ethereal wind speed, presupposing the exponential nature of this relation, can be approximated by the expression

WM (Z) = bWM 1 e  Z ;

(28)

where b = 1:136;  = 1:16 10 3 m 1 are proportion-

al ratios; WM is the speed values of the ethereal wind,

measured in [5, 6] at the altitude ZM ; Z is the altitude

above the sea level. The expression (28) enables by the

results [5, 6], obtained at the altitude ZM , to calcu-

late high-altitude speed relation of the ethereal wind

WM (Z) at the conducted near

latitude 'M Kharkov, at

. The measurements were the latitude 'K = 500 n.l.

The index \K ," as well as above, means the measure-

ment place. Supposing, that the nature of high-altitude

speed relation of the ethereal wind in this point of a

218

Yu.M. Galaev

terrestrial globe looks like to the relation (28), we shall write

WK (Z) = bWK (ZM) 1 e  Z ;

(29)

where WK (Z) is the horizontal speed component of the ethereal wind at the latitude 'K , at the altitude ZM , which can be determined as

Let's calculate
value WMmax 

the anticipated value 9000 m/sec represents

gWrK . The the average

value of the ethereal wind maximum speeds in the work

[5], measured during all months of observations. Having

put in (37) WM = WMmax and Z = ZK = 150 m (ZK

is the radiolink altitude over the sea level), we shall

receive gWrK = 6:4 m/sec m.

WK (ZM ) = W cos hK;

(30)

where hK is the apex altitude of the ethereal wind at the latitude 'K . It is possible to receive from the equations (27), (30), that

4. Instrumentation
The measurement method essence, adopted in this work, is described above. Let's notice the following.

WK (ZM ) = WM cos hK= cos hM:

(31)

Let's write down hK and hM through the apex declination value M and the latitude 'K , 'M . Let's take the ratio for transition from the rst equatorial system of astronomical coordinates to horizontal ones, [33]

The expression (1) introduces a processing algorithm of the received signal I . It was shown in the work [27], that at such processing of the sources instability of the carrier and modulating frequencies do not enter in (1) and do not in
uence on the value ' measurement accuracy. It has enabled to facilitate

cos h cos A = cos ' sin  + sin ' cos  cos t:

(32)

the creation and exploitation problem of the devices, intended for phase characteristics of radiolinks mea-

Here A is the apex azimuth in a horizontal system of surement, essentially. The self-excited generators with

astronomical coordinates; t and  is an hour angle, and parametric stabilization of their frequencies are applied

the apex declination in equatorial coordinate system at the way implementation as emission sources. The

accordingly; ' is geographic latitude of the observation way realised in radiowaves lengths range 8mm and ear-

place. In a point of the lower apex transit, as well as for any aster, A = 1800, t = 12h (in a degree measure t = 1800) [33]. In this case (32) becomes

lier was probed in [1{4]. The nal radiolink points were equipped with identical complete transceiver sets as well as the recording equipment. The transmission

cos h = sin ( + ') :

(33)

and sounding signals reception in each of the points were conducted with the same aerial. The aerials of

Let's substitute the values cosh, dened by the expression (33), in (31). Allowing the latitudes values are 'K , 'M and the value dened in [5] the apex declination M , we shall receive
WK (ZM ) = WM sin (M + 'K) = sin (M + 'M) :(34)

both points are identical and have mirrors of diameters 1,1m. The generators of carrier frequencies had the values frequencies about 37 GHz, and generators of modulating oscillations 0.5 GHz. The generators frequencies of carrier oscillations diered from each other in 50 MHz for radiated and received signals separation.

Then, allowing (34), the expression (29) will be like

WK

(Z

)

=

bWM

sin sin

(M (M

+ +

'K 'M

) )

1

e Z :

(35)

The expression (35) allows to calculate high-altitude relation of the ethereal wind speed horizontal component for the latitude 'K by the work results [5, 6], obtained at the altitude zM . As the radio link is declined from a meridian with the angle a, the high-altitude relation of the ethereal wind speed radial component in the radio link location, at the moment of a lower apex culmination is

The carrier frequency is f0A = 36:95 GHz in the point A, and the carrier frequency is f0B = 37 GHz in the point B . The resulting power of each transmission devices executed on Gunn's diodes, is about 70 mW. The generators of carrier and modulating oscillations with concomitant clusters are located in thermostats. The hardware complex contained the systems of the frequencies automatic tuning. The hardware has passed the comprehensive lab tests on a board and into the measuring complex structure within the environment temperatures -250C ... +350 C in dierent meteorological conditions. One-channel recorders were used for registration in both nal points. The additional

WrK

(Z)

=

bWM

cos



sin sin

(M (M

+ +

'K ) 'M )

1

e Z :(36)

We shall nd the high-altitude gradient relation of this speed, dierentiating (36) on a variable Z . We'll obtain

recorder was used in the point A and for amplitude registration of a received signal. This information allowed to distinguish the time periods, during which the hydrometeors (rain, snow) settled out, that was not always possible to determine visually. As well the amplitude channel executed the function of the work

gW

rK

(Z

)

=

bWM

cos



sin sin

(M (M

+ +

'K 'M

) )

e

Z:

(37)

continuous control of the measuring system. The analysis of the hardware actual characteristics and its test

Etheral wind in experience of millimetric radiowaves propagation

219

results have shown, that sa is the hardware resulting root-mean-square measurement error of the values does not exceed 2.40.

5. The radiointerferometer work

In the accepted measurement method according to (10) the measured value represents the dierence of phase invariants values of radiolink probing signals, received simultaneously in radiolink points. Allowing (9), (25), (26), we shall write the expression for as follows

=

k2

r+2

(1

R +

1 R2

R2 sin k0B 2R cos k0B

r+ r+)2

+

+

k2

r2

R (1 +

1 R2

R2 sin k0A 2R cos k0A

r r

)2 ;

(38)

where the indexes at k0A and k0B re
ect the dierence

of probing signals carrier frequencies, received in the

points A and B accordingly. The rst member of the

right part (38) represents the value 'A , the second represents the value 'B . The expression (38) is writ-

ten to conformity with the initial hypothesis position of

the ethereal wind northern apex. In this case the val-

ues r+ , r are determined by the expressions (25),

(26) accordingly and the measured value F should get

the positive values. Let's consider the work features of

the measurement method, which are stipulated by its

specic technical implementation.

We shall consider the isotropic case (Wup = Wl =

0), that corresponds to radiowaves propagation in

Aether, xed regarding the observer (radiolink) at the

presence of isotropic atmosphere within the adopted

hypothesis. (It is adequate to such medium as Aether

absence in nature within the modern generally accept-

ed imaginations.) In this case the radiowave propaga-

tion velocity does not depend on the radiation direc-

tion, but depends on the altitude above the Earth's

surface V (Z) = c=n(Z). As Wup = Wl = 0 and

gWr = 0, according to (25), (26), (24), we shall receive r+ = r = r. Then, if in (38) to suppose, that

k0B = k0A, we shall receive = 0 and this equalling,

according to a reciprocity principle, does not depend

on the interspace properties. However, the engineering

solution was accepted at this method implementation,

in which the carrier frequencies value of probing sig-

nals, emitted by each of radiolink points, diered. As
k0B = k0A , 6= 0, that we shall consider as the

measurements error. We shall identify the values

depending on the parameters change such as gn and R

with (38), (24). We shall estimate probable ranges of

the values change gn and ment. The average values m 1 in winter up to -5.95

R for the calculations full-

gn 10

8chmang1einfrosumm-m4.e2r5in10the8

air layer 25{50 m above the Earth's surface according

to the work data [30{32]. Such data take intermediate

values in spring and autumn. The values the average during the day as follows (-3,6 m 1 in winter and (-5,5 ... -6,4) 10 8 m

g.1.n.in-c4hs,au9n)mg1me0oern8.

According to the work [26], on 
at tracts with grass

covering, the values change of the re
ection coecient

module R is within the limits of 0.2 ... 0.5 on the wave

8 mm, in the season of active vegetation, up to 0.4 ...

0.7 after grass withering, remaining approximately the

same if there is a friable snow cover. Thus the highest

values of the re
ection coecient, reached 0.7 ... 0.8,

were noticed in the season of snow melting.

In the work, at errors calculating, the range of

the value R change is taken within 0.03 ... 0.07, that

is stipulated by the mentioned above features of the

re
ected wave formation in a radiolink. The selected

change range R is matched to its change range as to

the value, measured in the work [26], and includes the

value R = 0:; 04, which is determined in the work from

the eld vertical probing results in an experimental ra-

diolink (left-hand piece of the Fig. 3). Such probing was

executed at the end of summer, when the grass cover-

ing represented the withering green. It is possible to

suppose on the basis of the work results [26] and ver-
tical probing data, that the values R  (0; 04 0; 05)

are close to average value in a radiolink during the part

of the year, since September till January, in which the

measurements were executed. We shall use such change

range R at fullment of the ethereal wind parameters

estimations.

The calculation results of error values and '

values are presented on two pieces of the Fig. 4 depend-

ing on the gradient gn values for three values R.

Abscissa axis for these pieces is common. The values

gn and the values, conforming to them Deltar, are giv-

en for visualization on it. The conformity between these

values was established with the help (24). The values

and ' in grades were taken on ordinate axises.

On the lower piece, for R = 0:05, two curves are given,

i.e. 'A(gn) is the continuous line and 'B(gn) is

the broken line. As it is visible, the curves are shifted

regarding each other. It was stipulated by the values

dierence of probing signals carrier frequencies, as the

results in errors occurrence. The curves 'A(gn) and 'B(gn) represent the maxima and minima po-

sition of interference patterns in the points A and B .

(The analogue is the interference pattern in an optical

interferometer). The radio interferometer working sec-

tion, within which the measurements were conducted,

is indicated by the heavy straight line section in the

bottom part of the piece. The same relations for val-

ues R = 0:03 and R = 0:07 are re
ected in the piece

by the curves 'A(gn), shown only within the radio

interferometer working section. The errors calcu-

lation results, executed for three values R are given on

the upper piece of the Fig. 4. The value gn change

range is indicated by the broken line, i.e. the stroke

220

Yu.M. Galaev

Figure 4: The measurement error relation to the vertical prole gradient of the refraction coecient

Figure 5: The measured value relation to the ethereal wind velocity gradient

section in this piece bottom, which was determined from the works [30{32]. It follows from the Fig. 4 and calculations results, that the value changes in all the indicated gradient gn change range in the following limits: at R = 0:04 from min = 0:870 up to
max = 1:180; at R = 0:05 from min = 1:090 up to max = 1:430. The calculations have shown, that the error is systematic and can be considered as the correction.

The diurnal and seasonal variations of ambient tem-

perature can result in the radio link geometry change
| the value r0 change, and at f0A 6= f0B the er-

rors T occurrence is possible. It can be supposed,

that the radiolink length remains invariable, since the

radiolink nal points are arranged on concrete build-

ings, the foundations of which are in an ice-free soil

layer at almost constant temperature. Nevertheless,

the errors calculation DFT was executed in the suppo-

sition, that the whole radiolink was located on concrete

foundation with that the value galaev:tex T =

t5Th0e0Cle.n0A:g0t1hb0i1ti3lna0r0tg0heermet.errmIotprshearcasatnauproepcecrauarrnegadet,

altitudes temperature change of radiolink nal points.
T  0:050 at T = 500 C in this case. The cal-

culations are conducted at R = 0:07. As it is visible

the errors T are small, and they can be neglected. The executed analysis has shown, that the measurement method is tolerant practically in an isotropic case to change the environment parameters. The detected errors are insignicant and represent systematic displacement, which we shall consider as the correction.

In an anisotropic case (Wup > Wl > 0, that corresponds to the positions of the initial hypothesis) from (38), (25), (26) follows, that the measured value depends on a radial component gradient of the ethe-

real wind speed gWr and the value R. The calcula-

tion results 5 10 8 m

of 1

the are

relations given for

(gWr), executed at gn four values R in the Fig.

= 5.

The values are put in grades on an ordinate axis.

The curves family, given in the Fig. 5, allows to determine the values gWr by the value measurement results. As the value gWr is determined as a prole derivative Wr(Z), so the value is proportional to the ethereal wind Wr speed.

The expressions (38), (25), (26) demonstrate the relevant property of the accepted measurement method,

necessary for this research problem solving. The measured value is not equal to zero (the correction value is taken into account) only in the case, when two eects

of the ethereal wind, i.e. the anisotropy eect and the

Etheral wind in experience of millimetric radiowaves propagation

221

altitude eect, take place simultaneously. Really, it is
easy to see, that 6= 0 only when Wrup 6= Wrl 6= 0.
In other cases, when Wrup = Wrl (i.e. gWr = 0) or Wrup = Wrl = 0, the measured value = 0. In other words, the method is responsive to the Earth's relative movement and electromagnetic waves propagation medium | the Aether only in the case, if this medium will form a gradiant layer near the Earth's surface at the motion, i.e. if the medium shows the viscosity property | the property intrinsic to material mediums, which are derivated from separate fragments. Therefore, the anisotropic eects and altitudes can be found out with the reviewed measurement method in the unied measurement act. The space eect also can be found in this unied measurement act, as the same measurements results should be subjected to the averaging procedure in the sidereal time scale for periodic components detection.
6. The measurement technique
The probing signals IA and IB were emitted towards one another from the points A and B accordingly. Simultaneously the probing signals reception and their processing according to the adopted measurement way were performed in each of the points. The measured values 'A and 'B were recorded on the recorders' tapes in both points. The time marks were performed in the point A and were transmitted with the signal IA to the point B . These marks were recorded synchronically with both points of the recorders in such a way. The measurements were conducted continuously and around-the-clock. The instrumentation calibration and control of its operation implemented with the self-contained device, which performed the testing signal with controled parameters and the spectrum similar to the probing signal spectrum. Such operations were conducted at regular intervals, as a rule, 1 time for 1 operating hour.
7. The processing technique of measurement results
The measurement results processing of the values 'A and 'B included the calculation procedures of the measured value ; its diurnal variation within separate sidereal day d(S); its diurnal variation within sidereal day, averaged for the whole measurements cycle of
(S); root-mean-square deviations  . The values 'A and 'B were shown on separate chart tapes like continuous records. The signal amplitude record was used for the sites allocation, executed at hydrometeors falling. Such sites were removed from further processing. The sidereal time marks were synchro recorded on all tapes. The values 'A(S)

Table 1: Distribution of measurement time on months

of the year

Month of the year IX X XI XII I

Common

measurement

278 193 165 300 352

time (hours)

and 'B(S) readouts were made, they were recorded in the table of the conforming observations date from these tapes with the separate slide scale, in one hour of the sidereal time. In the same table, the values of the measured value (S) were recorded, calculated on the formula (10) for each of this sidereal day hours. The sequence of such numbers obtained for separate sidereal day, describes diurnal variation d(S). The calculated values were recorded in the other table. The average value of the measured one was calculated for each hour of this table sidereal day

(S)

=

1 

X  j=1

j (S);

(39)

where  is the quantity of the value readouts, made during the whole cycle of measurements, in the sidereal time equal to S . The root-mean-square deviations of values from its average value were calculated for each hour of the sidereal time with the following known expression [34]:



8 <
(S) =
:

1 X  h  j=1

j (S)

(S)i29=1=2 : (40)
;

8. Measurement results
The results are considered in the work, which were obtained during 5 months, since September 1998 till January 1999. The measurements were conducted aroundthe-clock, except both weekends and holidays as well as the cases, when the electric power was not supplied to one of the measuring points for technical reasons. The general time of continuous measurements was 1288 hours. The measurement time distribution on months of the year is shown in the Tab. 1.
The distribution of readouts quantity of the measured value on sidereal day time, for the whole measurement cycle (5 months), is shown in the Tab. 2.
In the Fig. 6 the examples of measurement result records, 9th November 1998 are shown.
The gure is composed from pieces mated in time of three chart tapes with the following values records: signal amplitudes, adopted in the point A (the upper curve); the phase invariant 'A, the phase invariant

222

Yu.M. Galaev

Figure 6: The example of registered values records

Table 2: Distribution of readouts quantity of the measured value on the sidereal day time Sidereal time (hour) 1 2 3 4 5 6 7 8 9 10 11 12 Quantity of readouts 53 54 55 54 54 50 50 52 51 52 53 53 13 14 15 16 17 18 19 20 21 22 23 24 51 52 54 55 57 54 54 57 55 55 55 58

'B (lower curve). The pieces illustrate the typical

changes of the registered values. Speeds of the chart

tapes drive are 20 mm/hour. The vertical strokes repre-

sent time marks in the gure. The digits under strokes

indicate the sidereal time value in hours. The time 
ow

direction is from right to left. The scale sections for

a signal amplitude change estimation in decibels and

phase invariant values change in degrees are marked in

the gure right section. The change of time dierence

between the values 'A and 'B , i.e. the change of the measured value = 'A 'B can be seen in the

gure. From the hour, the value

moment S = has changed

14 to

hou1r10u.p

to S = 21 The dier-

ence between values 'A and 'B 
uctuations can be

explained by the following. The radiowaves are propa-

gated in counter directions in a radio link. According to

the initial hypothesis, their propagation medium is the

Aether | material medium, having the properties of

viscous and compressible gas. The gradiant speed layer

is formed in the Aether 
ow at Aether motion near the

rough surface, as well as at motion of any viscous and

compressible gas, and such motion can be accompanied by this 
ow parameters 
uctuations. (Other causes of such 
uctuations are possible also).
The ethereal wind speed 
uctuations and this speed gradient gW result in values 
uctuations 'A and
'B . It follows from (25), (26) and lower pieces of the Fig. 4, that such 
uctuations are counter correlated. The radiowaves propagation in the Aether occurs in isotropic atmosphere available at the same time. Known atmosphere parameters 
uctuations [29] also will result in 
uctuations 'A and 'B . It follows from (23) and lower piece of the Fig. 4, that the 
uctuations gn result in the correlated 
uctuations of values
'A and 'B . Therefore, the 
uctuations of each values 'A and 'B within the adopted 
uctuation hypothesis are the 
uctuation superposition, stipulated by the indicated causes. Besides, it follows from (16),
(17), that gn+ 6= gn is at gWr 6= 0. In this case the ra-
diowaves refraction, distributing in the driving Aether in counter directions, is various. The radiowaves pathways pass with the distinguished characteristics in the

Etheral wind in experience of millimetric radiowaves propagation

223

Figure 7: Mean diurnal variation of the measured value
space eld, and the re
ecting sites on the Earth's surface are shifted regarding each other. It can result in the values 'A and 'B 
uctuation decorrelations. The reviewed features of the values 'A and 'B 
uctuations formation illustrate the distinctions available, which are visible in the Fig. 6.
The systematic measurement results were subjected to statistical processing. The mean diurnal variation of the measured value within sidereal day (S) is given in the Fig. 7
The sidereal time S in hours is marked on an abscissa axis, the measured value in grades is marked on an ordinate axis. The vertical strokes indicate condence intervals, dened as (S)  (S). It follows from a Fig. 7, that the measurement results are not denitely zero and are not accidental observation errors. The relation (S) has the expressed form of the varied value with the period, equal to one sidereal day, i.e. the measured eect has a space parentage. It is shown above, that the measured value is not equal to zero point only in the case when two eects of the ethereal wind, i.e. an anisotropies eect, stipulated by the Earth's relative movement and radiowaves propagation medium as well as the altitude eect, stipulated by the speed gradiant layer in this medium 
ow available, take place simultaneously. The positive measurement results, given in the Fig. 7, demonstrate, that these both required ethereal wind eects take place simultaneously. Therefore, the space eect development, the anisotropy eect and the

altitude eect are shown in the unied experiment, in the unied measurement act.
Let's compare the measurement results of the work to the results [5] and [11]. We shall use maximum ratings of the measured values at matching. We'll dene the values gWrK with the relations (gWr), which were given in the Fig. 5. We shall call such values gWrK to be measured. The measured gradient values of the ethereal wind speed horizontal component gWK can be found as follows

gWK = gWrK = cos ;

(41)

that follows from the expressions (35) - (37) results. The expression (37) allows to compare the measurement results of the work to the data [5, 11]. Really, having put in (37) Z = ZK can be found, that

WM

=

gWrK eZK sin (M + 'M b cos  sin (M + 'K)

)

:

(42)

The expression (42) allows to calculate the values WM with the measured values gWrK . We shall designate the values WM, calculated with (42), as WMK and treat this value as follows: WMK is the horizontal component of ethereal wind speed on the geographic latitude 'M , the altitude ZM , calculated by the measurements results of the ethereal wind velocity gradient at the latitude 'M and the altitude ZK .
Let's substitute the value WM , dened by (42), in (36). Let's receive, that the radial component of the ethereal wind speed in a radiolink can be determined with the following expression

WrK = gWrK eZK 1 =:

(43)

This speed horizontal component is equal accordingly to

WK = WrK= cos :

(44)

Calculated with (43), (44) we shall call also the val-

ues WrK and WK to be measured.

The parameters measurement results of the ethereal

wind and the work results [5, 11] are listed in Tab. 3.

The rst column of the Tab. 3 represents the value

m2,3ea,4suarreemtehnetscraelscuulltatio(nS)rmesauxltisn

grades. The columns of the ethereal wind

parameters executed with the expressions (41), (44),

(42) accordingly. The data about the ethereal wind

parameters are shown in the table like fractions. Mul-

tipair numerator corresponds to the parameter value

obtained at R = 0:04, and denominator - at R = 0:05.

Such form of the measurement results representation is

stipulated by those, that the systematic values R mea-

surement was not conducted during the experiments.

The digit in the column 2, given in brackets, represents

the calculated value gWK with (37), (41), that we shall

224

Yu.M. Galaev

1 , grade
14

Table 3: The ethereal wind parameters

2

3

4

5

g86W;;62K32 ;;

m=s m (9,05)

WK1140,11m49 /s

WM86K4192,04m/s

WM, m/s [5] 9000

6 WM, m/s [11]
6000

call as the anticipated ethereal wind velocity gradient value in Kharkov. The column 5 represents the maximal ethereal wind speed value, obtained by Miller at measurement results averaging, executed in the observatory Mount Wilson in April, August and September 1925 [5]. The column 6 represents the maximal ethereal wind speed value, measured in the observatory Mount Wilson in the experiment [11], 1929.
The executed estimations have shown, that the horizontal component of ethereal wind speed reaches the
value WK  1414 m/s in Kharkov. This work measure-
ment results are recalculated to the observatory Mount Wilson location with the expression (42). The obtained
value WMK  8490 m/s, that is close to the result [5]
WM = 9000 m/s. A bit smaller values WMK (allowing the estimations at R = 0:05), in comparison with the result [5], can be explained with dierent conditions of the experience realization. The cross-country terrains measurement are conducted on the slightly cross terrain. The ambient relief altitudes dierence is about 20 m. The experiment [5] was executed at a mountain top and the ambient terrain was much below the measurement conducting place. It can be supposed, that in the rst case the terrain ambient relief aect on the ethereal wind speed value is more, than in the case of the work [5]. Such supposition about the surface and local subjects in
uence (hills, buildings, located closely to the radiolink, etc.) has been conrmed at the results comparison [5] and [11]. So, the ethereal wind speed smaller values in [11] in comparison with the data [5] are explained in [7] by Aether 
ow deceleration with buildings walls, in which there was this work author's interferometer [11]. Miller [5] built a light wooden house for the measurements realization in the observatory Mount Wilson. There were continuous windows made of white canvas on all its sides. In 1929 Michelson, Peas, Pearson [11] conducted the similar experiment in a fundamental building of an optical workshop in Mount Wilson observatory. The ethereal wind measured speed was no more than 6000 m/s as a result.
The ethereal wind speed value, measured in a radio frequency band at the work, is close to the ethereal wind speeds values, measured in electromagnetic waves optical range in the experiments of Miller [5, 6], Michelson, Peas, Pearson [11]. Such comparison results can be considered as mutual conrmation of the research results veracity, the experiment [5, 6] and the experiment [11].
The ethereal wind velocity gradient measurements

were not performed in former works, we can compare the measured values gWK with the anticipated (calculated) value. As we can see from the table 3 (column 2) the value gWK measurement results are close to its calculated value.
The executed analysis has shown, that this work results can be explained by radiowaves propagation phenomenon in a space parentage driving medium with a gradiant layer speed in this medium 
ow near the Earth's surface. The gradiant layer available testies that this medium has the viscosity | the property intrinsic material media, i.e. media consisting of separate particles. Thus, the executed experiment results agree with the initial hypothesis positions about the Aether material medium existence in the nature.
9. Conclusion
The parameters measurement method of anisotropic media of electromagnetic waves propagation was oered and realised in the range of millimeter radiowaves at the work. The systematic experimental research results, executed near the Earth's radiolink of a line-of-sight, have shown:
| the Earth's relative movement and radiowaves propagation medium available;
| the radiowaves propagation medium 
ow has a space origin;
| the radiowaves propagation medium has the viscosity | the property intrinsic to material media consisting of separate particles.
The work results can be considered as the experimental hypothesis conrmation about the existence of such material medium, as the Aether, in the nature.
References [1] Yu.M. Galaev, B.V. Zhukov, F.V. Kivva, \The pass-
band variability of a ground communication circuit of millimeter radiowave range." Scientic instrument manufacture in mm. and sub. mm. radiowaves frequency bands: Digest of scientic works Kharkov: Institute of radiophysics and electronics engineering of NSA in Ukraine. 1992, pp. 63{72. [2] F.V. Kivva, Yu.M. Galaev, \Dispersion eects in frequency windows of mm wave range radio waves." Atmospheric Propagation Technical Exchange Proceedings: ARL, Orlando, FL, USA. 1993, pp. 509{517.

Etheral wind in experience of millimetric radiowaves propagation

225

[3] Yu.M. Galaev, \Model of radiowave dispersion in atmosphere." Atmospheric Propagation and Remote Sensing III: Edited by Walter A.Flood and Walter B.Miller, Proc. SPIE 2222. 1994, pp. 851{861.
[4] Yu.M. Galaev, F.V. Kivva, \A wideband communication line of millimeter radiowaves band . Experiment. Model." 7-th International Crimean conference \Microwave technique and telecommunication technologies" (CrMiCo 97). The conference papers: Sevastopol, Crimea, Ukraine. 2, 1997, pp. 670{673.
[5] D.C. Miller, \Signicance of the ether-drift experiments of 1925 at Mount Wilson." Science, LXIII, No. 1635, pp. 433{443 (1926).
[6] D.C. Miller, \The ether-drift experiment and the determination of the absolute motion of the Earth." Rev. Modern. Phys., 3, 203{242 (1933).
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[8] A.A. Michelson, \The relative motion of the Earth and the Luminiferous ether." The American Journal of Science, III series, XXII, 128, 120{129 (1881).
[9] D.C. Miller, \Ether-drift experiment at Mount Wilson." Proc. Nat. Acad. Amer., 11, 306{314 (1925).
[10] S.I. Vavilov, \New \ethereal wind" searches." Successes of physical sciences, 6, 242{254 (1926).
[11] A.A. Michelson, F.G. Pease, F. Pearson, \Repetition of the Michelson - Morley experiment." Journal of the
Optical Society of America and Review of Scientic In-
struments, 18, 3, 181{182 (1929). [12] R.J. Kennedy, \A renement of the Michelson - Morley
experiment." Proc. Nat. Acad. Sci. of USA, 12, 621{ 629 1926. [13] K.K. Illingworth, \A repetition of the MichelsonMorley experiment using Kennedy's renement." Physical Review, 30, 692{696 (1926). [14] E. Stahel, \Das Michelson - Experiment, ausgefurt im Freiballon." Die Naturwissenschaften, Heft 41, 8, 10, 935{936 (1926). [15] G. Joos, \Die Jenaer Widerholung des Mihelsonversuchs." Ann. Phys., 7, 385{407 (1930). [16] V.A. Atsukovsky, \General etherdynamics. Simulation of the material and eld structures on the basis of the imaginations about the gas like Aether." Moscow, Energoatomizdat, 1990, 280 pp. [17] L. Essen, \A new ether drift experiment." Nature, 175, 793{794 (1955). [18] J.P. Cedarholm , G.F. Bland , B.L. Havens , C.H. Townes, \New experimental test of special relativity." Phys. Rev. Letters, 1, 9, 342{349 (1958). [19] D.C. Cyampney, G.P. Isaac, M. Khan, \An ether drift experiment based on the Mssbauer eect." Phys., Letters, 7, 241{243 (1963). [20] T.S. Jaseja, A. Javan, J. Murray, C.H. Townes, \Test of special relativity or of the isotropy of space by use of infrared masers." Phys. Rev., 133a, 1221{1225 (1964).

[21] W. Azjukowski, \Dynamik des Athers." Ideen des exakten Wissens, Stuttgart, 2, 48{58 (1974).
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[23] A.A. Michelson, H.G. Gale, Assisted by F. Pearson. \The eect of the earth's rotation on the velocity of light." Part II. The Astrophysical Journal, LXI, 5, 140{ 145 (1925).
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[26] G.P. Kulemin, V.B. Razskazovsky, \Dissipation of millimeter radiowaves by the Earth's surface at small angles." Kiev, Nauk. dumka, 1987, 232 pp.
[27] A.s. 1337829 USSR, MKI4 G01R29/00. \The measurement way of radiotracts characteristics." / Y.M. Galaev, B.V. Zhukov, Bul. ed., 34, 183 (1987).
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[31] E.E. Vyaltseva, \Variability of the air refraction index for a MWF in a 300-m layer in winter." Ed. IEM, 1974. Iss. 6 (44), pp. 99{105.
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Spacetime & Substance, Vol. 2 (2001), No. 5 (10), pp. 226{229
c 2001 Research and Technological Institute of Transcription, Translation and Replication, JSC

BROAD STATIC STARS CLASS MODELLING
WITHIN ONE APPROACH
Alexandre Baranov1 and Michael Lukonenko2
Krasnoyarsk State University, Depatment of Theoretical Physics, 79 Svobodny Avenue, Krasnoyarsk 660041, Russia

Received November 30, 2000

A class of static spherical stars is considered. The Einstein equations with energy-momentum tensor in perfect 
uid

approximation x = r=R; R is

and the

with the radius of

mass density distribution (x) star). By means a method of

s=ucce0s(s1ive

xa2pp)rnoxaimreatsioolnvsedw(ith0

a

is a center density, small compactness

parameter  = 2M=R (M is mass of star) the analytical solution of approximative Einstein's equations for integer

value of n parameter is received. Models of three fundamentally dierent astrophysical objects are considered. These

are a neutron star (n = 1,  = 1,  = 0:147), the white dwarf Sirius B (n = 5,  = 1,  = 1:3 10 4 ), stars of

main sequence such as the Sun (n = 1,  = 1,  = 4:2 10 6 ). Analysis of stability given models is conducted.

Such critical parameters of considered star models as greatly possible mass, minimum star radius, greatly possible

compactness is determined. Results of calculations with known observational data were correlated.

1. Introduction

At modelling of such astrophysical objects as stars, frequently it is possible to not take into account dynamic processes account into them running. The necessity of the account of changes arises then, when the star or rotates, or fast loses the mass at the expense of radiative sublimation of the matter [1] and radiation. In other cases the physical description of stars in the assumption of their static character is admissible.
In the present article the descriptive attempt of physical star properties for dierent types of stars within the framework of one approach is realized. At modelling except for static character of a star, it suggests its spherical symmetry. The space-time geometry of such object interior gravitational eld we shall describe by a 4-interval
ds2 = F (r)dt2 + 2L(r)dtdr r2(d2 + sin2d'); (1)

where functions F (r) and L(r) are metric coecients. We use here a geometrical system of units in which velocity of light and gravitational constant are equal to unit. The Einstein equations are solved with a energy-momentum tensor in perfect non-viscous 
uid approximation and with the mass density distribution inside a star as

(x) = 0(1 x2)n;

(2)

1e-mail: bam@lan.krasu.ru 2e-mail: mvl@krw.ru

where 0 is an energy (mass) density at the star centre; x = r=R; R is the star radius; n,  are parameters.
We have chosen this type of mass density distribu-
tion not accidentally. For n = 0 and f = 1; n = 1g
Einstein equations are solved analytically. If n = 0, we have the interior Schwarzschild solution [2], and if
f = 1; n = 1g, we have an exact solution for parabolic
mass density distribution [3].

2. Mathematical model

For 4-interval (1) and energy-momentum tensor in perfect non-viscous 
uid approximation, with mass density distributions (2), Einstein equations will look as follows

"=1

Z x

(x)x2 dx;

(3:1)

G00

+

d dx


ln

p"
x



G0

+

"0x

+ 2(1 2x2"

") ;

(3:2)

p~0 =

p~2

x 2"

+

p~

"

1 2x"

~x2



+

~(" 2x"

1)

;

(3:3)

w8hRer2e;

" = F=L2; G = pF ;
p(x) is a pressure; a

p~ = p; ~ = ;  = prime means derivative

on x.

The central of energy density0 is connected with

a central pressure p0 by means the Fermi degenerated

relativistic gas equation of state . The junction con-

ditions together of an interior gravitational eld of the

Broad static star class modelling within one approach

227

star with a eld of an exterior solution Schwarzschild give following relations:
"(x = 1) = 1 ; p(x = 0) = 0 (4:1)
G(x = 1) = p1 ; G0(x = 1) = 2p1  (4:2)
where  = 2M=R is the star compactness; M is the star mass.
Now we have system (3) with three equations and four unknown functions. These function are (x), p(x), "(x), G(x). For closing given system of equations we shall add to it the mass density distribution (2).
Thereby, expressions (2-4) describe the mathematical model of our problem. Given model has no analytical solutions under integer values of parameter n > 1.

3. Integration of Einstein equations

For integer values of parameter n we may multiply out

of the expression (2) by means the formula of binomial

theorem. Then equation (3.1) is integrated and we have

relation

"(x) = 1  (x)=(1)

(5:1)

with

(x)

=

X n j=0

Cnj

( 2j

1)j +3

x2j+2

(5:2)

and following equality

 = 0(1):

(6)

In the expression (5.1), constant of integration is put equal to zero for restriction of function "(x) in the star center. Equality (6) permits to inroduce the parameter
 in the system equations (2-4). For real stars   1
(for example, for the Sun J = 4 10 6) and we may

construct an analytical approximate solution of system

(2-4) by the progressive approximations method. It is

a main idea of our paper.

We (x) =

de(xn)=e(fxu2nc(t1io))n.

(x) for further calculations as

Thus,

"(x) = 1  x2 (x):

(7)

On physical sense the function is the ration of average mass density of the star interior part with radius x > 0 to the total star average mass density.
Substitution of equality (7) in equation (3.2) gives

(G0=x)0 = Q(x);

(8)

where Q(x) = x (x)G00(x) + x 0(x)G0(x)=2 + 0(x)G(x)=2:

We shall nd the solution of equation (8) as series on compactness:

G(x) = X 1 kGk(x):

(9)

k=0

Using method to mathematical inductions, it is possible to prove validity of following formulas

G0k+1=x 0 = Qk(x);

(10:1)

G0 = 1;

(10:2)

where

Qk(x) = x

(x)G0k0(x) + x

0 (x)G0k(x)=2 +

0(x)Gk(x)=2: (10:3)

Expression for function F (x) may be written now

in the following form

F (x) = X 1 kFk(x) = G2(x)
k=0

(11:1)

with

G2(x)

=

X 1

0
@k

X k GjGk

1
jA:

k=0

j=0

(11:2)

Integrating twice expression (10.1), nally is obtained

Fk

(x)

=

X k Q~j

(x)

+

C1(j)x2=2

+


C2(j)

j=0





Q~k j(x) + C1(k j)x2=2 + C2(k j) ;

(12:1)

where

F0 = 1;

Z Z



Q~j(x) = x Qj(x) dx dx;

(12:2) (12:3)

C1(j) C2(j) are constants of integration. These constants are dened on each step k of iterations from the functions Fk(x) junction conditions on the star surface with external Schwarzschild eld

F (x = 1) = 1  ) Fk(x = 1) = k0 k1; (13:1)

F 0(x = 1) =  ) Fk0(x = 1) = k1;

(13:2)

wheTrehuskj,

is the Kronecker symbol. the expressions (12) are the

formulas

of

the

function F (x) progressive approximations method over small parameter  . That the integrand functions in

(12.3) represent the sums of various real degrees x, we

have no problems with calculation of analytical expression for k-approximation function Fk(x) accoding to formula (12.1).

228

Alexandre Baranov and Michael Lukonenko

Table 1: Parameters of prototyped stars

Type of star

R [cm]

M [MJ]

[g=sm0 3]

n

A B C

1 2:02 6:96

1101060190

1 0:89
1

1 1:3

11001150

1 5

142:54 25

Type of A

stsrTabpl50e:[8d24i:nR=1se0ms3u32l]t

of modelling Vsound(x =
0:21

0)[c]

B C

2:38 3:46

1100262

6:68 1:64

10 10

3 3

We shall nd an approximate expression for the

sFe(cxon)=dLm2(xet)riacnfdacetqouralLit(yx()7,)u. sEinspgetchiaellryelwaetioshnal"l(mx)ar=k

that function

F (x) = X 1 Fk(x)

(14)

k=0

is the exact solution of system equations (2-4) under

choice of mass density as (2). This solution has appro-

ximate character then, when summation over k in (14)

is produced up to a xed value.

4. Real stars modelling

From boundary conditions (4.1) on function "(x) and equality (6) the relation follows

X n j=0

( 1)j 2j + 3

=

2M 80R3

:

(15)

One allows to coordinate parameters n and  in the left-hand part with physical characteristics of the star.
We obtained the following values of parameter n (at  = 1) for dierent three types of stars. Type A is a neutron star, type B is a white dwarf (the Sirius B) and type C is a star of main sequence (the Sun).
The values of parameter n in Tab. 1, have some inaccuracy, connected with properties of the equality (15). The left-hand part of this equality is discrete, but right part is continuous. Therefore not always there is a possibility to select for a concrete star an integer value of parameter n, satisfying (15).
Under the formula (12) the analytical expression of an approximate solution of the system of equations (24) for three types of stars was obtained (Tab. 1). Central values of pressure and sound velocities Vsound were obtained as the result of our modelling.
Results of calculations were correlated with known observational data. For example, for the Sun model we have following facts, described in [4]:

1. value p0 from Tab. 2 diers from known on 2% ;

Table 3: Limiting values of compactness n 012345 max 0:14 0:21 0:20 0:18 0:16 0:14

Table 4: Critical parameters of stars
fn; g M [MJ] R [km] f0:2; 1g 1:65 16:69 f1:4; 1g 0:85 9:58 f2:6; 1g 0:62 7:43 f3:8; 1g 0:52 6:39 f1:0; 1g 0:46 5:78 f20; 1g 0:30 3:66 f1; 0:2g 1:65 16:69 f1; 1:4g 0:85 9:58 f1; 2:6g 0:62 7:43 f1; 3:8g 0:46 6:39 f1; 1:0g 0:42 5:78 f1; 20g 0:30 3:66

2. value of pressure on boundary of the solar kernel (x = 0:25) on the order is less central value;
3. value of the mass density on boundary of the solar kernel on the order is less central value.

5. Stability of model

We investigated of the model stability domain in the
space of parameters fn; ; g with using following cri-
terions of stability:

1. Oppenheimer{Volko criterion of stability [5]: dM=d0 < 0;
2. principle of the energy domination: p= < 1=3;

3. principle of the causality: Vsound < 1.

Thus, we have got restriction on maximum of com-

pactness max for These restrictions

xed values are in Tab.

of 3.

parameters
f = 1; 0 

n n

and
 5g

 .

.

The stability criterion

dM=dR < 0;

(16)

is equivalent to Oppenheimer{Volko criterion. This criterion allows to nd maximum of star masses M and minimum of star radii R , which characterized by xed values of parameters  and n. These restrictions
for f = 1; 0  n  5g and fn = 1; 0:2    20g are
located in Tab. 4. Comparing modelling data (Tabs. 1, 2) and restric-
tion on use of model (Tabs. 3, 4, 5) we may conclude about applicability of this approach to broad class of

Broad static star class modelling within one approach

229

stars { from neutron stars and white dwarves up to the main sequence of stars.
Let's note that in paper [6] the star models with the energy density distribution of the type (2), however
consideration was limited by f = 1; n = 1; 2; 3g.
6. Conclusion
In summary, it is necessary to note that the choice of the mass density distribution as type (2) does not restrict applicabilities of our method. For realization of successive approximations method it is necessary to integrate the expressions (3.1) and (12.3) only.
The paper is realized in framework of the Federal program of Russia \Astronomy."
References
[1] A.M. Baranov, N.N. Paklin, Izv.Vuz.(Fizika), 10, 13-17 (1994). (in Russian)
[2] J.L. Singe, \Relativity: the General Theory," Foreign Literature, Moscow, 1963, p.244 (in Russian).
[3] A.M.Baranov, Dep. in VINITI 13.07.76, 2626-76 (in Russian).
[4] \Physical encyclopedic dictionary," eds. A.M. Prohorov, Soviet encyclopedia, Moscow, 1983 (in Russian).
[5] J.R. Oppenheimer, G. Volko in: \Albert Einstein and general relativity," Mir, Moskow, 1979, p.337 (in Russian).
[6] H. Knutsen, Gen. Rel. and Grav., 22, 925-946 (1967). [7] A.M. Baranov, M.V. Lukonenko, S.F. Tegai, Abstracts
of Intern. Confer. \Geometrization of Physicis III", \Hater", Kazan, 1997, 6 (in Russian).


Spacetime & Substance, Vol. 2 (2001), No. 5 (10), pp. 230{232
c 2001 Research and Technological Institute of Transcription, Translation and Replication, JSC

ON FIXED SINGULARITIES IN KERR-SCHILD SPACES
Alexandre Baranov1 and Sergei Tegai1
Krasnoyarsk State University, Depatment of Theoretical Physics, 79 Svobodny Avenue, Krasnoyarsk 660041, Russia
Received November 30, 2000

Kerr theorem is used to obtain possible kinds of xed singularities in Kerr-Schild spaces with geodesic and shear-free

nofulslqcuornegprouleinnocem. iaFl.unTchtieondisFcr(iGm;in1a;nt2)ofdtehteermpoilnininogmiimalpdliecsitclryibtehseconmulml coonnsgirnugeunlcaeritiiseschoofotsheen

in the general form electromagnetic and

gravitational elds. It is shown that all xed singularities are intersections of two second order sufaces. For example

the ring singularity of Kerr-Newman solution is an intersection of a sphere and a plane passing through the center

of the sphere. With the square form of function F the Kerr-Newman solution is the only one with xed singularity

nite in the three-space.

1. Intoduction

The Kerr-Shild space is described by

g =  2Hkk;

(1)

where  is Minkowskian metric; H is a scalar function; k is a null vector for both metrics g and  :

gkk = kk = 0:

(2)

Consider only the spaces assuming geodesic and shearfree null congruence with tangent vector k. By Kerr theorem [1] a geodesic and shear-free null congruence can be given by

kdx = Gd + G+ GGdv + du;

(3)

where u; v = x0 x3; ;  = x1 ix2 and G(u; v; ; ) is implicitly determined by

F (G; 1; 2) = 0:

(4)

F (G; 1; complex

2) is an variables

arbitrary analytic G; 1 = G + u; 2

function of = vG + :

three

Common singularities of the electromagnetic and

gravitational elds are given by dF=dG = 0. Solu-

tions with singularities bounded in three-space are of

the most interest for star exterior modelling.

2. Linear case

General linear form of function F (G; 1; 2) is

F = a11 + a22 + a3G + b1:

(5)

1e-mail: bam@lan.krasu.ru

The condition for singularity

dF=dG = a1 + a2v + a3 = 0

(6)

is a system of two real linear equations. Both describe

three-dimentional hyperplanes in four-space. So the

singularity can't be nite in linear case.

3. Square case

General square form of function F (G; 1; 2) is F = b112 + b212 + b31G + b422 + b52G + +b6G2 + c11 + c22 + c3G + d1: (7)

The condition dF=dG = 0 is equivalent to the equiation

D = 0; where D is a discriminant of square polinomial

F (G).

Only xed singularities are considered later. This

means degree

that D must not depend polinomial all it's terms

ownitxh0:xA04s;

xD03ixs ia;

xfo0u2xrtih2

and others containing x0 must be equal to zero. All the

discriminant's the form (b22

t4ebr1mb4s)(oxf 0f2ourtxh12degxre3e2

caxn4b2)e2w. rAitntdenthine

terms of the third degree can be written in the form

(x02 x12 x22 x32)

[(2b2(b3 + c2) 4b1b5 4b4c1)x0 (2b2(b5 + c1) 4b3b4 4b1c2)x1

i(2b2(b5 c1) 4b3b4 + 4b1c2)x2 +

+(2b2(b3 c2) 4b1b5 + 4b4c1)x3]:

So the demand of xed singularity leads to the dis-

criminant of only the second degree. This complex dis-

criminant gives the intersection of two real second order

surfaces with additional requirements

b22 4b1b4 = 0;

(8)

On xed singularities in Kerr-Schild spaces

231

b2(b3 + c2) 2b1b5 2b4c1 = 0;

(9)

b2(b5 + c1) 2b3b4 2b1c2 = 0;

(10)

b2(b5 c1) 2b3b4 + 2b1c2 = 0;

(11)

b2(b3 c2) 2b1b5 + 2b4c1 = 0;

(12)

4b1b6 4b4d1+b23+c22+2b2c3 4b5c1+2b3c2 = 0;(13)

2b2(d1+b6)+2(b1+b4)c3 (b3 c2)(c1 b5) = 0;(14)

i[2b2(d1 b6)+2(b1 b4)c3 (b3 c2)(c1+b5)] = 0;(15)

4b1b6 + 4b4d1 + b23 c22 = 0;

(16)

4c1b6 4b5d1 + 2(b2 + c2)c3 = 0;

(17)

where (13)-(17) are the coecients with x02; 2x0x1; 2x0x2; 2x0x3; x0 correspondingly. These constraints

lead to the following cases:

1 b2 = b1 = b4 = 0:

1.1) b3 c2 = 0:

1.2) b3 c2 = 1:

2

b222..;12))b1bc;31 b6=6=4

are not equal

0; 0;

b5 c2

6= 6=

0; 0;

b3c2 b3c2

to = =

zero b5c1 b5c1

at the

6= 6=

c3: c3:

same

time.

2.3) b3 = b5 = c1 = c2 = 0:

2.4) b3c2 = b5c1 = b2c3:

3.1. b2 = b1 = b4 = 0

With the notation a0 = b3 c2; a1 = b5 c1; a2 = i(b5 + c1); a3 = b3 + c2 equations (13) - (16) take the simple shape of

a21 + a22 + a23 = 0

(18)

and

a0a1 = a0a2 = a0a3 = 0:

(19)

1.1 If a0 = 0 the characteristic quadric form D~ of the discriminant has the shape of

D~ = a21x1+2a+22xa212a+2xa1x2a23+x2ax13a3+xa1x23x33+2:

(20)

The singularity described by it is a line. The linear part of the discriminant in
uence only on the location of the line and can be easily eliminated by linear substitution of coordinates.
1.2 In this case we get the Kerr-Newman solution [2]. The discriminant has the form of

D = (x12 +2((b6

d+1)xx212++ix(b362)++dc123)x2

4b6d1 + + c3x3):

(21)

It's real part is a sphere and it's imaginary part is a plane passing through the center of the sphere. There intersection is a ring singularity of the Kerr-Newman solution.

3.2. b2 6= 0; b1 6= 0; b4 6= 0

The equations (9)-(12) are linear and homogeneous on

variables b2; b1; b4 . So b2; b1; b4 are not simultaneously equal to zero only when the rank of the system is less

then three. This is equivalent to

4(b3c2 b5c1) = a20 a21 a22 a23 = 0:

(22)

The equations (13) - (17) are also the system of linear equatons on variables b2; b1; b4. The solution of this system exists only if

c23 4b6d1 = 0:

(23)

With (8) and (22) this gives us the degenerate complex quadric form D~ . The singularity in this case is a line.
2.1 For b2 6= 0; b3 6= 0; b5 6= 0 we obtain from (9) -
(12), (22)

b1

=

b3 2b5

; b4

=

b5 2b3

;

c2

=

b5c1 b3

;

(24)

2b6 = 2c3b4 + (b3 c2)b5;

(25)

2d1 = 2c3b1 (b3 c2)c1:

(26)

Characteristic quadric form D~ of the discriminant is

proportional to

D~  (b23

b25)2x12 2i(b23 b25)(b23 + b25)x1x2 4b3b5(b23 b25)x1x3 (b23 + b25)2x22 +
+4ib3b5(b23 + b25)x2x3 + 4b23b25x32: (27)

Both real and imaginary parts of it have eigenvalues

[0; (b3b3)2 + (b5b5)2; (b3b3)2 (b5b5)2]:

(28)

2.2 Analogously with 2.1 we obtain

b1

=

c1 2c2

; b4

=

c2 2c1

;

b5

=

c2b3 c1

:

(29)

With equations (25), (26) this gives us the quadric form

D~  (c21

c22)2x12 4c1c2(c21

2i(c21 c22)(c21 c22)x1x3 (c21

++ cc2222))x2 1xx222

+

+4ic1c2(c21 + c22)x2x3 + 4c21c22x32 (30)

and it's eigenvalues

[0; (c1c1)2 + (c2c2)2; (c1c1)2 (c2c2)2];

(31)

b4

2.3 In this case = f1b6; c3 =

we can 2f22d1;

assume b6 =

b1 = f1d1; b2 f2d1 , where

= f1

f6=1c30;

because all of bi are not equal to zero, and we have

D~  (1

f22)2x12 4f2(1

2i(1 f22)x1x3

f22)(1 (12

+ +

ff2222))x21xx222

+

+4if2(1 + f22)x2x3 + 4f22x32: (32)

2.4 In this case D is identically equal to zero. F = ((b5v + b3 + b3b5)G + b3u + b5 + b5c1)2: (33)

Singularity is innite by the same reasons as in linear case. For xed singularity b5 = 0:

232
4. Conclusion
We see that for square form (7) of function F (1; 2; G) there are two kinds of singularities. First is the ring singularity of the Kerr-Newman solution and the second one is a line. So we can conclude that for obtaining of nonstationary solutions by Kerr-Schild method we need to choose higher degree of F or consider the singularities depending on time.
The paper is realized in framework of the Federal program of Russia \Astronomy."
References [1] D. Cramer, H. Shtefany, M.McCallum, E. Herlt,
\Exact solutions of Einstein equations," Energoizdat, Moscow, 1982 (in Russian). [2] R.P. Kerr, W.B. Wilson Gen. Rel. and Grav., 10, 273 (1979).

Alexandre Baranov and Sergei Tegai


Spacetime & Substance, Vol. 2 (2001), No. 5 (10), pp. 233{235
c 2001 Research and Technological Institute of Transcription, Translation and Replication, JSC

ALGEBRAIC CLASSIFICATION OF 5D KRISHNA
RAO WAVE SOLUTION
Alexandre Baranov1 and Nikolai Bardushko2
Krasnoyarsk State University, Depatment of Theoretical Physics, 79 Svobodny Avenue, Krasnoyarsk 660041, Russia

Received December 14, 2000

The Krishna Rao 5D genaralized solution's wave properties by means of the Weyl curvature tensor algebraic classication which was introduced earlier by one of authors are investigated. It was shown that 5D metric belongs to the algebraic class similar to Petrov's type II of 4D space-time algebraic classication while the initial 4D metric is type N.

1. Introduction
In general relativity wave solutions investigation is one of the most important problems. The same metric in various coordinates looks dierently. Sometimes it is dicult to say, whether the solution of the Einstein equations belongs to a wave type or not. As a rule on this problem there can not be an answer basing only on appearance of the metric. So it is necessary to use special invariant methods for detection of wave properties of space-time.
Petrov's algebraic classication of gravitational elds is such method in 4D space-time [1]. Here we consider space-time as space with a time-like direction both 4D and 5D space-times. Using a symmetry of the curvature tensor subscripts the Riemann tensor of 4D space-time into symmetrical traceless complex 3 3 the Weyl matrix may be mapped. An eigenvalues problem of such Weyl matrix solves the task of algebraic classication of gravitational elds in 4D space-time. Depending on Weyl matrices' eigenvalues and eigenvectors we have seven matrix canonical subtypes, i.e. in 4D space-time only seven various algebraic subtypes of gravitational elds exist or total three types by Petrov [1].
It is known that gravitational elds of various types on Petrov have dierent the Segre characteristics of the Weyl matrix. The analysis of wave criterions in 4D space-time was investigated in details in [2]. In that classication wave solutions correspond to algebraically special types N and III as rule. The Segre characteristics of the Weyl matrices are [(2 1)] and [(3)] respectively and type N describes pure gravitational wave. Sometimes type II is considered as a wave algebraic type. In
1e-mail: bam@lan.krasu.ru 2e-mail: cut cut@mail.ru

reality the type II describes mixed gravitational elds with wave propeties and has the Segre characteristic of the Weyl matrix [2 1]. The Weyl matrix canonical form of the type II is a sum of two canonical Weyl matrices: type D and type N.
2. On 5D algebraic classication
Maximum data on the space-time structure can be obtained from the curvature tensor of Riemann. That is why it is so important to extend the 4D Petrov's algebraic classication onto 5D space-time of Kaluza. An attempt of such extension and algebraic classication of some solutions was undertaken in [3]. According to this approach the conformal curvature tensor of Weyl from the Kaluza space-time is mapped to symmetrical traceless 10 10 Weyl matrix and the 5D space-time is mapped to 10D manifold of bivectors. Then it is solved the matrix eigenvalue problem in general case to classify the Kaluza space.
3. Krishna Rao generalized solution
Metric element of the 5D space-time we will take as ds2 = e2k(dt2 d2) 2d'2 dz2 e2mdu2; (1)
where k = k(t ); m = m(t ): This metric element generalizes Krishna Rao wave
solution [4] onto 5D Kaluza-Klein theory. Let us to classify corresponding Weyl tensor by means of ideas from [3].

234

Alexandre Baranov and Nikolai Bardushko

At rst we have got to use orthonormalized 1-form basis to follow the method [3]. So we construct it as

(0) = ekdt; (1) = ekd;

(2) = d'; (3) = dz;

(2)

(5) = emdt:

Nonzero conformal curvature Weyl tensor components in basis (2) are

W(0)(1)(0)(1) W(0)(2)(0)(2) W(0)(2)(1)(2) W(0)(3)(0)(3) W(0)(3)(3)(1) W(3)(1)(3)(1) W(1)(2)(1)(2) W(0)(5)(0)(5) W(0)(5)(1)(5) W(1)(5)(1)(5)

= = = = = = = = = =

WA((2)B(3)+(2)4(3k_)

=

W(3)(5)(3)(5) m_ );

A(B 4k_);

A(B + 2k_ m_ );

A(B + 2k_);

A(B + 2k_ + m_ );

A(B 4k_ m_ );

A(B 2k_ m_ );

A(2B 2k_);

A(2B 2k_ + m_ );

=

m_ A;

(3)

W(2)(5)(2)(5) = 3m_ A;

where

A

=

e 2k 6

;

B = 2(m + m_ 2

2k_m_ ):

Weyl tensor may be mapped onto 10D bivector manifold by following manner. Each pair of antisymmetrical subscripts is represented as a new subscript. This subscript rule of mapping is

01 ! 1; 02 ! 2; 03 ! 3; 23 ! 4;

31 ! 5; 12 ! 6; 05 ! 7; 15 ! 8;

(4)

25 ! 9; 35 ! 10:

The mapping reduces the Weyl tensor to symmetrical traceless 10 10 Weyl matrix

W=

(5)

w1

w2

w3

w4

w5

w1

w5

w6

w3

w7

w8 w9

w9 w10

w11

w1

Here only nonzero components are shown and w1 = W(0)(1)(0)(1); w2 = W(0)(2)(0)(2); w3 = W(0)(2)(1)(2); w4 = W(0)(3)(0)(3); w5 = W(0)(3)(3)(1); w6 = W(3)(1)(3)(1); w7 = W(1)(2)(1)(2); w8 = W(0)(5)(0)(5); w9 = W(0)(5)(1)(5); w10 = W(1)(5)(1)(5); w11 = W(2)(5)(2)(5):

The matrix (5) has a box structure according to [3]. Each box of matrix (5) represents dierent physi-
cal elds in 4D space-time: W f1::6; 1::6g describes the gravitation; W f1::3; 6::10g corresponds to the electric eld; W f3::6; 6::10g corresponds to the magnetic eld; W f6::10; 6::10g corresponds to a scalar eld.
Now we set put an eigenvalue problem for the Weyl matrix (5),

detjW Ij = 0;

(6)

where matrix

I = diag( 1; 1; 1; 1; 1; 1; 1; 1; 1; 1)

is a mapping of the tensor g()()g(
)() g()(
)g()() according to the subscript rule(4).
Elementary transformations of {matrix are rotations of basis (2) in 5D. By means of such elementary transformations {matrix may be reduced to canonical form

W() = diag(1; 1; p1; p1; p1; p21; p21; p2; p3; p4);

(7)

where diagonal components of {matrix (7) are the elementary divisors of eigenpolinomial (6) with their multiplicity and

p1 =  1 =  m_ A;

p3 =  p4 = 

p2 =  3 =  4 = 

2 =  ( 3m_ A);
q
( k_ m_ 17k_2 + 8Bk_ )A;
q
( k_ m_ + 17k_2 + 8Bk_ )A;

Segre characteristic in this case is

[(11)(122)111]:

(8)

A metric with the characteristic (8) belongs to algebraically special metric types . Our {matrix (6) has elementary divisors with double multiplicity.
As well as in the Petrov algebraic classication let us call it as II type. In this case every elementary divisor has its eigenvector. Eigenvectors are lightlike if they belong to the elementary divisors with double multiplicity or more. Eigenvectors in the 10D manifold dene invariant directions in 5D space-time. The lightlike bivectors correspond to light-like invariant directions. So the algebraic classication may be used to determine wave structure of space-time. If a space-time is described by the Weyl matrix (5) with elementary divisors of double multiplicity or more then it has wave structure.
The considered 5D space-time with the metric element (1) has the Weyl matrix's (5) elementary divisors of double multiplicity (see (5)). These divisors correspond to following lightlike bivectors

e1 e2

= =

(0) (0)

^ ^

(2) (5)

+ +

(1) (1)

^ ^

(2); (5):

(9)

Algebraic classifcation of 5D Krishna Rao wave solution

235

Bivectors (9) dene lightlike directions in 5D spacetime

l1 l2

= =

(1) (5)

; :

(10)

Thus 5D space-time with metric (1) has wave structure and the Krishna Rao generalized solution preserves its wave structure, but it is more general solution.
In 4D space-time the Krishna Rao metric belongs to the type N of Petrov's algebraic classication. For this type of space-time the Weyl matrix has elementary divisors with double multiplicity and eigenvalues which are equal to zero.
To have complete correspondence in 5D space-time with the 4D algebraic classication we should require

=

m_ 6

e

2k

= 0:

(11)

The equation (11) determines N-type for the 5D spacetime with metric element (1).

4. Energy-momentum tensor

It is easy to see that in 5D space-time the Ricci tensor for the metric (1) is not equal to zero. Using the generalized 5D Einstein's equations

R()() g()()R = kT()();

(12)

we may write nonzero components of the energy-momentum tensor for the Krishna Rao generalized solution (1) in the orthonormalized basis (2) as

0 T(0)(0)T(0)(1) T()() = BBBB@ T(0)(1)T(1)(1)

1

0 T(3)(3)

CCCCA ; (13)

0

where R is scalar curvature; ;  run 0; 1; 2; 3; 5 and

T(0)(0) = (B 2m_ + k)=; T(0)(1) = (B + k_)=;
T(1)(1) = (B + 2m_ + k)=; T(3)(3) = 2m_ e 2k=:
It is seen that the energy-momentum tensor has wave structure, i.e. it has lightlike eigenvectors. According to an algebraic classication of symmetric second rank tensors the tensor (13) belongs to the class II of such classication.

5. 4D projection

To investigate observable properties of 5D space-time with metric element (1) let us produce a 4D projection, i.e. a projection on 4D space-time. This 4D-projector may be easy written in 5D form as

4g = g

g5g5 g525

;

(14)

or using the equation (1) we have 4D metric element

4ds2 = e2k(dt2 d2) 2d'2 dz2;

(15)

which is the Krishna Rao 4D metric for the pure radiation.

6. Conclusion
The wave properties of the 5D Krishna Rao's generalized solution have been investigated. We used an approach which is written in [3] and permits to generalize the 4D Petrov algebraic classication on 5D Kaluza space-time. It was shown that new 5D metric belongs to algebraically special type (in the sense of the 5D algebraic classication), analogous to the type II of the Petrov classication. The research of physical meaning of the 5D energy-momentum tensor is a problem of following investigation. The algebraic classication of 5D spaces may be used to systematize space-times, to analyze and to search new solutions.

References
[1] A.Z. Petrov, \New methods in general relativity," Nauka, Moskow, 1966, 495 p. (in Russian).
[2] V.D. Zakharov, \Gravitational waves in the Einstein theory of gravitation," Nauka, Moskow, 1972, 199 p. (in Russian).
[3] A.M. Baranov, Izv.Vuz.(Fizika), No.3, 73-78 (1995) (in Russian).
[4] D. Cramer, H. Shtefany, M.McCallum, E. Herlt, \Exact solutions of Einstein equations," Energoizdat, Moscow, 1982, p. 211-212 (in Russian).


Spacetime & Substance, Vol. 2 (2001), No. 5 (10), pp. 236{240
c 2001 Research and Technological Institute of Transcription, Translation and Replication, JSC
Spacetime & Substance
Contents of issues for 2000{2001 years
Vol. 1 (2000), No. 1 (1) ADDRESS TO THE READERS (1). A. Einstein. ON THE ELECTRODYNAMICS OF MOVING BODIES (2). Yu.S. Vladimirov. THE GRAVITATION AND BINARY GEOMETROPHYSICS (15). N.A. Zhuck. THE IDENTITY OF INERTIAL AND GRAVITATIONAL MASSES IS PROVED! (23). N.A. Zhuck. THE COSMIC MICROWAVE BACKGROUND AS AGGREGATE RADIATION OF ALL STARS
(29). N.D. Kolpakov. THE DISCOVERY OF POLARIZATION WAVES AND PROBLEMS OF PHYSICS (35). V.E. Kats, A.V.Pashkov. ABSOLUTE SIGN SYMMETRY (41). DISCUSSION (44). THE QUESTIONNAIRE (44). THE UKRAINIAN-RUSSIAN GRAVITATIONAL CONFERENCE (45). RESEARCH AND TECHNOLOGILAL INSTITUTE OF TRANSCRIPTION, TRANSLATION AND
REPLICATION (47).
Vol. 1 (2000), No. 2 (2) THE EDITORIAL BOARD (49). A. Einstein. THE EQUATIONS OF THE GRAVITATIONAL FIELD (51). Bijan Saha. SOLITONS OF INDUCED SCALAR FIELD AND THEIR STABILITY (53). V.Ya. Vargashkin. ANALYSIS OF HIP #54268 PHENOMENON AS THE EARLIEST FROM CANDIDATES
TO GRAVITATIONAL MICROLENS (60). N.A. Zhuck. GRAVITATIONAL VISCOSITY AND GEODETIC CURVATURE OF THE UNIVERSE (71). Vasile Ureche and Rodica Roman. THE KEPLER`S THIRD LAW IN GRAVITATIONAL MANEFF`S FIELD
(78). V.A. Smirnov, G.I.Kuzjmenko. COSMOGONY AND EVOLUTION OF COMET AND METEOR SUB-
STANCE IN THE SOLAR SYSTEM (81). A.V. Snagoschenko and S.V.Bondarenko. PHILOSOPHICAL PROBLEMS OF FUNDAMENTAL CON-
CEPTS: \PERPETUITY", \GRAVITATION" (86). THE UKRAINIAN-RUSSIAN CONFERENCE \GRAVITATION, COSMOLOGY AND RELATIVISTIC
ASTROPHYSICS" (90).

Spacetime & Substance, Vol. 2, No. 5 (10), 2001

237

DISCUSSION (96). NEW BOOKS (96).

Vol. 1 (2000), No. 3 (3)
The 1-st Scientic Conference \NEW CONCEPTS ABOUT WORLD AND STRUCTURE OF SUBSTANCES"
(October 30, 1998, RTI TTR, Kharkov, Ukraine) The Conference Proceedings (In Russian)
INTRODUCTION (97) N.A. Zhuck. NEW CONCEPTS ABOUT THE UNIVERSE AND ITS LAWS (98). N.D. Kolpakov. NEW PHYSICS (105). V.V. Balyberdin, N.A. Zhuck. PROSPECTS OF EXPERIMENTS ORGANIZATION ON DEFINITION OF
MEDIAL DENSITY OF THE UNIVERSE AND VELOCITY OF POLARIZATION WAVES (110). V.M. Kontorovich. MERGINGS OF GALAXIES AS THE CAUSE OF QUASARS PHENOMENON (114). M.F. Khodjachich. COSMOLOGICAL PERIODICITIES IN RADIOSPECTRUMS OF QUASARS (121). A.V. Archipov. ARCHAEOLOGICAL RECONNAISSANCE OF MOON (126). A.P. Volchenko. ABOUT THE NEW APPROACH TO CONSTRUCTION OF THE SPECIAL RELATIVITY
(130). Yu.A. Bogdanov. PRACTICAL RESULTS OF FIELD INTERACTION OF NATURAL OBJECTS (135). V.I. Balabay. THE CHARACTERISTICS OF A PHYSICAL VACUUM AND METHODS OF THEIR MEA-
SURING (138).

Vol. 1 (2000), No. 4 (4)
The Ukrainian-Russian Conference "GRAVITATION, COSMOLOGY AND RELATIVISTIC ASTROPHYSICS"(GRAV-2000)
(November 8-11, 2000, Kharkov, Ukraine, Kharkov National University) Part 1. The separate reports in English
SCIENTIFIC PROGRAM (145). S.A. Belousova. THE DESCRIPTION OF THE HADRON SPIN POLARIZABILITIES BY THE COVARIANT
LAGRANGIAN AT LOW ENERGIES (151). Justin Chashihin. DIMINUTION OF COSMIC DISTANCES SOLVES PROBLEMS OF SOLAR NEUTRI-
NOS, SUPERLUMINAL EXPANSION AND GALACTIC HALOS (153). Justin Chashihin. QUANTUM SOLUTION OF SINGULARITIES PROBLEM IN GENERAL RELATIVITY
(157). Justin Chashihin. AN IDEA FOR DIRECT EXPERIMENTAL MEASUREMENT OF THE SPEED OF
GRAVITATIONAL INTERACTION (161). A.K. Guts. THE RELATION OF UNCERTAINTY FOR RADIUS OF THE UNIVERSE (163). D.V. Kattzyn, E.V.Saveljev. CONFORMITY IN THE SOLUTIONS OF EINSTEIN EQUATIONS FOR
MODELS OF THE MULTIVARIATE UNIVERSE, FILLED WITH SUBSTANCE (165).

238

Contents of issues for 2000{2001 years

D.L. Khokhlov. ON THE FLATNESS AND HORIZON PROBLEMS (168). Doris Kiekhoven. GRAVO-INERTIAL FIELD THEORY (170). Volodymyr Krasnoholovets. SPACE STRUCTURE AND QUANTUM MECHANICS (172). Rasulkhozha S. Sharaddinov. ON THE GRAVITATIONAL FIELD OF THE ELECTRIC CHARGE (176). K.N. Sinitsyn. THE "BLACK HOLES" AND NATURE OF "DARK MATTER" IN THE BINARY MODEL
OF DISTRIBUTION OF THE DENSITY SUBSTANCE AND NATURE OF GRAVITY (179). K.N. Sinitsyn. THE BINARY MODEL OF DISTRIBUTION OF THE DENSITY SUBSTANCE AND NA-
TURE OF GRAVITY (182). N.A. Zhuck. FIELD FORMULATION OF THE GENERAL RELATIVITY AND COSMOLOGY (186). V.A. Zykunov. SPIN EFFECTS OF THE W-PRODUCTION IN HADRON-HADRON COLLISIONS (191).

Vol. 1 (2000), No. 5 (5)
The Ukrainian-Russian Conference \GRAVITATION, COSMOLOGY AND RELATIVISTIC ASTROPHYSICS" (GRAV-2000)
(November 8-11, 2000, Kharkov, Ukraine, Kharkov National University) Part 2. The separate reports in Russian
M.M. Abdildin, M.S. Omarov, M.E. Abishev. ON THE ORBITAL STABILITY OF THE MOTION PROBLEMS IN GR (193).
M.M. Abdildin, M.E. Abishev. INTEGRATION OF THE EQUATION OF ROTATION MOTION IN PROBLEM OF TWO ROTATED BODIES IN GR (194).
A.S. Bogdanov. PROBLEM OF THE SEARCH OPTICAL CANDIDATES ON THE IDENTITY WITH GRB (196).
A.A. Chernitskii. THE POSSIBILITY OF UNIFICATION FOR GRAVITATION AND ELECTROMAGNETISM IN NONLINEAR ELECTRODYNAMICS (199).
S.S. Sannikov-Proskurjakov, M.J.F.T. Cabbolet. RENORMALIZED NEWTONIAN CONCTANT AGAINST EQUIVZLENCE PRINCIPLE (203).
N.D. Kolpakov. POLARIZATION WAVES AND PROBLEM OF THE GRAVITATION (207). M.F. Ozerov, A.E. Kochetov, L.V. Verozub. ABOUT GRAVITY FORCE EXPERIMENTAL TESTING
IN THE METRIC-FIELD GRAVITATION EQUITIONS (215). O.V. Sharypov, E.A. Pirogov, S.G. Grishin. RELATIVISTIC QUANTUM-GRAVITATIONAL HYPOTHE-
SES AND SPACE-TIME STRUCTURE (219). F.T. Shumakov. CREATION OF THE RELATIVISTIC GRAVITATIONAL CONCEPT OF MODEL OF THE
UNIVERSE (224). A.V. Snagoschenko, S.V. Bondarenko. PHILOSOPHICAL PROBLEMS OF FUNDAMENTAL CONCEPTS:
\PERPETUITY," \GRAVITATION" (229). V.R. Terrovere. KLEIN'S FUNDAMENTALS OF THE SPECIAL RELATIVITY (233). N.A. Zhuck. COSMOLOGICAL EFFECTS IN BULKY MICHELSON INTERFEROMETERS (235). I.I. Zima, G.F. Bogdanov. CORONAL OF THE HOLE AND ROTOR MAGNETIC WAVES (238).

Spacetime & Substance, Vol. 2, No. 5 (10), 2001

239

Vol. 2 (2001), No. 1 (6)
L.I. Petrova. THE ROLE OF CONSERVATION LAWS IN EVOLUTIONARY PROCESSES (1). N.A. Zhuck. FIELD FORMULATION OF THE GENERAL RELATIVITY AND PROBLEMS OF COSMOL-
OGY (24). N.D. Kolpakov. POLARIZATIONS WAVES AND PROBLEM OF GRAVITATION (31). Arbab I. Arbab. A COASTING UNIVERSE WITH VACUUM ENERGY (39). Jo. Guala-Valverde. THE IDENTITY OF GRAVITATIONAL MASS/INERTIAL MASS. A SOURCE OF
MISUNDERSTANDINGS (42). Sergey Siparov. COSMIC MASER AS A REMOTE QUANTUM DETECTOR OF THE GRAVITATIONAL
WAVES: ON THE POSSIBILITIES OF THE OMPR-BASED METHOD (44).

Vol. 2 (2001), No. 2 (7)
Afsar Abbas. ON THE ORIGIN OF THE UNIVERSE (49). Arbab I. Arbab. THE EVOLVING UNIVERSE AND THE PUZZLING COSMOLOGICAL PARAMETERS
(51). Arbab I. Arbab. LARGE SCALE QUANTIZATION AND THE ESSENCE OF THE COSMOLOGICAL
PROBLEMS (55). W.B. Belayev. COSMOLOGICAL MODEL WITH MOVEMENT IN FIFTH DIMENSION (63). L.C. Garcia de Andrade. METRIC AND DENSITY PERTURBATIONS IN WORMHOLE GEOMETRY
WITH SPIN-TORSION DENSITY IN FRW UNIVERSES AND THE VIOLATION OF THE WEC (66) M.E.X. Guimar~aes, L.P. Colatto and F.B. Tourinho. ON THE WEAK-FIELD APPROXIMATION IN
GENERALIZED SCALAR-TENSOR GRAVITIES (71). V.L. Kalashnikov. X-MATTER INDUCED COSMOLOGICAL SCENARIOS IN THE RELATIVISTIC THE-
ORY OF GRAVITY (75). Jozef Sima and Miroslav Sukenk. BLACK HOLES | ESTIMATION OF THEIR LOWER AND UPPER
MASS LIMITS STEMMING FROM THE MODEL OF EXPANSIVE NONDECELERATIVE UNIVERSE (79). V.R. Kurbanova and A.B. Balakin. EXACTLY INTEGRABLE MODEL OF DYNAMICS OF VECTOR BOSONS AND BIREFRINGENCE INDUCED BY CURVATURE (82). I.M. Galitsky. ABOUT NEW PHYSICS (PRINCIPLES) (84). DISCUSSION (95).

Vol. 2 (2001), No. 3 (8)
V.L. Rvachev and K. Avinash. QUADRATIC RED SHIFT LAW AND THE NON-ARCHIMEDEAN UNIVERSE (97).
B. Dragovich and Lj. Nesic. ADELIC QUANTUM COSMOLOGY (100).

240

Contents of issues for 2000{2001 years

A.K. Mittal, Daksh Lohiya. CONDITIONAL COSMOLOGICAL PRINCIPLE AND FRACTAL COSMOLOGY (104).
Alexandre Baranov and Dmitri Baranov. STATIC STAR MODEL AND MATHIEU FUNCTIONS (108). H. Chavez, L. Masperi, M. Orsaria. SUPERHEAVY PARTICLES EITHER FOR UHECR OR FOR MUON
ANOMALY (111). Jacques Moret-Bailly. POINTLESSNESS AND DANGEROUSNESS OF THE QUANTUM MECHANICS
(116). Miroslav Sukenk and Jozef Sima. PODKLETNOV'S PHENOMENON | GRAVITY ENHANCEMENT
OR CESSATION? (124). G.B. Alaverdyan, A.R. Harutyunyan, Yu.L. Vartanyan. ON SMALL MASS HYBRID STARS WITH
QUARK CORE (129). M.M. Abdildin, M.E. Abishev, N.A. Beisehova. ON SUBSTANTIATION OF RELATIVISTIC EQUA-
TION OF ROTARY MOTION IN GR MECHANICS (132). Ali Shojai and Fatimah Shojai. QUANTUM EFFECTS AND CLUSTER FORMATION (134). Jorge Guala-Valverde and Pedro Mazzoni. THE UNIPOLAR MOTOR: A TRUE RELATIVIST ENGINE
(140). DISCUSSION (143). NEW BOOKS (144).

Vol. 2 (2001), No. 4 (9)
The 1-st International Scientic Seminar \THE THEORETICAL PREMISES AND EXPERIMENTAL FACTS OF GRAVITATIONAL
SCREENING OF A SUBSTANCE" (April 26{27, 2001, RTI TTR, Kharkov, Ukraine)
The Seminar Proceedings PROGRAM OF THE 1-ST SCIENTIFIC SEMINAR (145). V.R. Terrovere. KLEIN'S FOUNDATIONS OF THE UNITED THEORY OF FUNDAMENTAL INTERAC-
TIONS AND PROBLEM OF GRAVITATIONAL SCREENING (147). N.A. Zhuck. PROPERTIES OF THE YUKAWA POTENTIAL AND GRAVITATIONAL SCREENING OF A
SUBSTANCE (153). A.A. Chernitskii. DIRECT VARIATION OF SPACE-TIME METRIC BY ELECTROMAGNETIC FIELD
(161). K.N. Sinitsyn. ON THE IDEA OF GRAVITATIONAL SHIELDING OF MATTER IN BINARY MODEL (164). Volodymyr Krasnoholovets. ON THE MASS OF ELEMENTARY CARRIERS OF GRAVITATIONAL IN-
TERACTION (169). S.A. Sannikov-Proskuryakov, M.J.T.F.Cabbolet. TOWARDS THE ETHER THEORY (APOLOGY OF
THE ETHER) (171). N.A. Zhuck. ON THE UNITED NATURE OF GRAVITATIONAL, ELECTROMAGNETIC AND NUCLEAR
INTERACTIONS (175). V.I. Balabay. DIFFUSION MODEL OF THE PHYSICAL VACUUM AND ITS EXPERIMENTAL CONFIR-
MATION (181). V.Ph. Tihonov. POLARIZATION MODEL OF HYDROGEN ATOM (189).

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Spacetime & Substance

Volume 2, No. 5 (10), 2001

CONTENTS

N.A. Zhuck, V.V. Moroz, A.M. Varaksin. QUASARS AND THE LARGE-SCALE STRUCTURE OF THE UNIVERSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Yu.M. Galaev.
PROPAGATION

E. .T.H. .E.R. A . .L.

.W . .I.N.D. .

I.N. .E. X . .P. E. .R.I.E.N. .C.E. .O. .F.

.M. I.L. L. .IM . .E. .T.R. I.C. .R. .A.D. .IO . .W . .A.V. .ES211

Alexandre Baranov and Michael Lukonenko. BROAD STATIC STARS CLASS MODELLING WITHIN ONE APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

Alexandre SPACES . . .

Baranov .........

and ....

Sergei Tegai. .............

.O. .N.

.F.I.X.E. .D.

.S.IN . .G. U . .L.A. .R.I.T.I.E.S.

.I.N.

.K.E. .R.R. -.S.C. .H.I.L.D230

Alexandre Baranov and Nikolai
KRISHNA RAO WAVE SOLUTION

B. .a.r.d.u.s.h.k. o. ..

.

A . .L.G. .E.B. R . .A.I.C. .C. .L.A.S. S. I.F. I.C. .A.T. I.O. .N.

.O.F. .

5.D233

Spacetime & Substance. Contents of issues for 2000{2001 years . . . . . . . . . . . . . . . . . . . . . . 236