ternational In ysical Ph Journal - orgonelab.org · UKR AI NE Kha rk i v Spacetime & Substance...

U K R A I N E K h a r k i v

Spacetime &Substance

International Physical Journal

Volume 2, No. 5 (10), 2001

c 2001 Research and Technological Institute of

Transcription, Translation and Replication

JSC

Spacetime &SubstanceInternational 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, Translationand Replication, JSC, ander Licence of the series DK, No. 184, issued by the State Committee forInformation 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)| Editor-in-chief

V.V. Krasnoholovets (Ky��v, Ukraine)| Vice Editor

M.M.Abdildin (Almaty, Kazakhstan)L.Ya. Arifov (Simferopol, Ukraine)Yu.A. Bogdanov (Kharkiv, Ukraine)B.V. Bolotov (Ky��v, Ukraine)M. Bounias (Le Lac d'lssarl�es, France)J.L. Buchbinder (Tomsk, Russia)

P. Carlos (Rio de Janeiro, Brazil)M.J.F.T. Cabbolet

(Eindhoven, Holland)P. Flin (Krakow, Poland)J. Gil (Zielona Gora, Poland)N.D. Kolpakov (Kharkiv, Ukraine)I.Yu. Miklyaev (Kharkiv, Ukraine)V. Mioc (Bucharest, Romania)Z.G. Murzakhanov (Kazan, Russia)Lj. Ne�si�c (Ni�s, Yugoslavia)

P.G. Niarxos (Athens, Greece)V.I. Noskov (Moscow, Russia)V.L. Rvachev (Kharkiv, Ukraine)S.S. Sannikov-Proskurjakov

(Kharkiv, Ukraine)V. Skalsk�y (Trnava, Slovakia)R. Triay (Marseilles, France)V.Ya. Vargashkin (Oryol, Russia)Yu.S. Vladimirov (Moscow, Russia)

(The list is not �nished)

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

Subscription information:The price of one paper unit (in US Dollars) is 2.0 in Ukraine; 2.4 in NIS* states; 10.0 in all other countries.

The electronic version price is 25 % of the paper version price.*) NIS (New Independent States without Ukraine) are Azerbaijan, Armenia, Byelorussia, Georgia, Kazakhstan,

Kirghizia, Moldova, Russia, Tadjikistan, Turkmenistan, Uzbekistan.

Accounts: In US Dollars

Correspondent: THE BANK OF NEW YORKEastern Europe DivisionOne WAll Street, New York, NY 10286Account No. 890-0260-610Bene�cialry Bank: UKRSIBBANK of UkraineIn favour of ZEMELNY BANK JSCAccount No. 1600-8-50174-01-00SWIFT: KHAB UA 2KBene�ciary: NTI TTR JSCAccount No. 26009011415

In UA Hryvnyas

Account No. 26009011415in KHAB ZEMELNY BANK,MFO 351652,AO NTI TTR,Cod 24473039,Kharkov, Ukraine(for Ukraine subscribers,

at the rate of the

National Bank)

The corresponding confermation as to the paying should be sent to the Editorial O�ce by E-mail.

Editorial O�ce: Zhuck N.A., RTI TTR, 3 Kolomenskaya St., Kharkov 61166, UkraineTel.: +38 (0572) 19-55-77, (044) 265-79-94. Tel./fax: +38 (0572) 409-298, 409-594, 141-164, 141-165E-mail: [email protected], [email protected], [email protected]. http://spacetime.narod.ru

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

Spacetime &Substance, Vol. 2 (2001), No. 5 (10), pp. 193{210c 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 mesheswith the medial size about 50{100 Mps, which like a foam homogeneously �ll all apparent part of the Universe isdetermined. 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 wasdetermined by formula r = R0 ln(1+z) , where R0 is the constant for the Universe, which equal about 1026 m. Next,investigation of quasars spatial distribution in spherical and cartesian co-ordinates is carried out. The Universe partmost explored with the help of telescopes and radio telescopes were chosen for this purpose. Delone triangulation iscarried 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 shownthat: for large distances (noticeably are more than 100 Mps) quasars in the chosen part of the Universe withoutdependence from distances and angular standing in space have averages of distribution, root-mean-square diversionand correlation factors, typical for a uniform distribution of random quantities; in smaller gauges the quasars aregrouped in thin walls of meshes (size about 100 Mps), reminding the lather; the quasars allocation in meshescorrelates with galaxies allocation; the Universe has no precise boundaries even on distance in 30{40 billions lightyears. General scienti�c and weltanschauung signi�cance of discovery that it is cardinally changes our representationabout global structure and development dynamics of the Universe as a single whole to con�rm the concept of thestationary inconvertible Universe and to reject concept dynamic dilating Universe which erroneously formed in theXXth century and taking the beginning from a so-called the Big Bang, which ostensibly has taken place of 12{15billions years ago.

1. Introduction

At present, the o�cial science adheres to the common-ly accepted concept that the Universe appeared 12{15billion years as a result of the Big Bang of the sub-stance which had been in tremendously dense and hotstate. After that the substance expanded, cooled down,split into the matter and the electromagnetic �eld andformed galaxies which are believed to continue movingfarther apart until now.

Such a model is based on the non-steady solutionsof the Einstein equations obtained by Soviet geophysicsand mathematician Fridman at the beginning of the1920s and the concept of the exploding commencementin the dynamics of the Universe advanced by Americanphysicist Gamov at the end of the 1940s.

The objective properties of the Universe, which al-legedly con�rm this model, are the discovery of the redshift in the spectra of galaxies by American astronomerHubble in 1929 and the Cosmic Microwave Background

1e-mail: [email protected] at the scienti�c seminar in the Kharkiv National

Technical University of Radioelectronics (Kharkiv, UKRAINE)

Radiation at the temperature 2.7 K by American radioastronomers Wilson and Pansias in 1965. It is con-sidered that the allocation of quasars in the Universecon�rms the Big Bang too (see Appendix I).

The �rst discovery was interpreted by scientistsas the result of the motion of galaxies away from eachother and the second discovery was construed as the re-mainder (relic) of the electromagnetic radiation whichhad segregated from the initial substance and thencooled down to the said temperature during the expan-sion of the Universe.

The above-mentioned properties of the Universe, in-cidentally, are not the direct evidence of its expansion.For instance, the decrease in the frequency of lightcan be the result of either the expansion of the Uni-verse or the dissipation of the energy of light when itspread at great distances, while the osmic MicrowaveBackground Radiation can be either the remainder ofthe high-temperature explosion of the super dense sub-stance or the total radiation of all stars of the stationaryUniverse with the said dissipation of the energy of light.

As a result of many errors, the modern o�cial cos-mology, 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 constructalternative cosmology by digging around the founda-tions of physics and re-shaping its superstruction. Asa consequence, a new stationary model of the Uni-verse, which takes into account the more re�ned lawsof physics (or their new interpretation), has been con-structed (see Appendix II).

The Universe represents a giant physical laborato-ry, in which fundamental physical theories are veri�ed.Cosmology is one of the tools of this laboratory. Thesubject of study of cosmology is the General Relativityis one of the two theories, on which the construction ofmodern physics (the second theory is quantum theory)is based. Perhaps it is this major role that cosmologyplays in the life of mankind.

The new cosmological model is con�rmed by 40properties of the actual Universe (observations or re-sults of experiments). The quasars are the farthestvisible objects of the Universe (Appendix I). They areexcellent object for investigation by means of the newstationary model of the Universe.

2. Initial database on quasars andtransformation of their coordinates

The researches of quasars were carried out not onlythrough telescopes. The considerable interest for re-searches was represented the �xed coordinates of al-ready discovered quasars. The statistical researches ofquasar distribution in space in increase process of quan-tity of discovered quasars gave the more and more in-teresting results.

The database on 23760 quasars was used for ourinvestigation, in which two angular coordinates (�; ')and redshift of radiation spectrum (z ) for each quasarare presented [41]. The fragment of an initial databaseis presented in Tab. 1.

Distance up to each quasar by redshift was deter-mined by formula

r = R0 ln(1 + z); (1)

where R0 is constant typical for the Universe approx-imately equal in 1026 m (see Appendix II). R0 = 1 isassigned for calculating of distances up to quasars andfor build-up of �gures.

The formula (1) is derived out of the distributionlaw of light at a large distance

� = �0 e�

r

R0 : (2)

It is the very important formula. We presentedtwo derivation of this formula in Appendix III and Ap-pendix IV.

Table 1: Fragment of the initial databaseNo. RAJ2000 DEJ2000 z

"h:m:s" "d:m:s"1 00 00 01.3 -02 02 00 1.3562 00 00 02.8 -35 03 33 0.5083 00 00 05.6 -27 25 10 1.9304 00 00 09.9 -30 55 30 1.7875 00 00 10.2 -31 59 50 1.6386 00 00 12.0 +00 02 24 0.4797 00 00 12.9 -02 10 25 1.4508 00 00 16.3 -31 44 38 1.4529 00 00 17.4 -08 51 23 1.25010 00 00 20.2 -32 21 01 1.27511 00 00 22.9 -02 27 15 0.59012 00 00 23.7 +02 12 41 0.81013 00 00 24.4 -12 45 48 0.20014 00 00 24.8 -30 50 49 1.46515 00 00 36.0 -31 19 25 2.013... ... ... ...

23760 23 59 59.3 +08 33 54 0.084

Calculation of quasars coordinates in spatial spher-ical coordinates is carried out by the formulas (in radi-ans; the corner '1 is measured from North Pole)

� =

��h +

�m

60+

�s

3600

�� 12; (3)

'1 =�

2� ' � �

180; (4)

where

' =

8><>:

'd +'m60

+'s3600

if 'd � 0;

'd � 'm60

� 's3600

if 'd < 0:(5)

Calculation of quasars coordinates in spatial carte-sian 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 co-ordinates by increment of distance up to quasars andfor cartesian coordinates by increment of coordinate Z(for convenience of investigations).

The preliminary investigations have shown thatthe observed quasars locate on the coelosphere non-uniformly. Especially it concerns those places whereNorth 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 ofquasars allocation

It is considered that density of a spatial distribution ofquasars is fast incremented in range of values z �= 2�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 andradio telescopes were chosen for this purpose. Delonetriangulation is carried out for laminas, its thicknessis appreciably less than the revealed meshes of large-scale quasars structure (the multitude of lines pairingeach quasar to its nearest neighbors without their mu-tual crossing is constructed). Thus the particular setof distances between quasars has turned out. Furtherthe statistical processing of set of these distances was

carried out.

In the beginning we have separated a thin layer ofthe Universe in a plane of the Earth equator (planeOXY, the axis 0Z is directed to the North Pole, Fig. 2).Further we chose the most explored areas of the Uni-verse for the analysis. Here we shall show two typicalareas 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 132quasars are in the area 2.

Allocation of the quasars in the area 1 is shown inTab. 2 and allocation of the quasars in the area 2 isshown in Tab. 3.

As have shown these investigations, average values,standard deviations and correlation factor practically


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 1Description Calculation TheoryMean mx -0.7307693464 -0.75Mean my 0.05896529208 0.05Standard-deviation �x 0.1415179730 0.1443375673Standard-deviation �y 0.1364377974 0.1443375673Linear-correlation kxy 0.1089561031 0

Table 3: Allocation of the quasars in the area 2Description Calculation TheoryMean mx -0.8062837008 -0.8Mean my -0.4992200605 -0.5Standard-deviation �x 0.05747427049 0.0577350269Standard-deviation �y 0.06059568292 0.0577350269Linear-correlation kxy -0,1016258970 0

coincide with similar parameters of uniform distribu-tion of random quantities, i.e. with the theory. It is im-possible to term these results and results of other sim-ilar investigations as ordinary accidental coincidence.Obviously that we have the facts con�rming that thequasars are distributed uniformly in the Universe, andthe Universe is stationary.

Next, the investigation of quasars allocation withinthe concept of the Big Bang of the Universe was car-ried out with determining of distances to each quasarin accordance with redshift but the method generallyaccepted in cosmology.

The investigations have shown that at the secondmethod of distances de�nition:

a) quasars density grows to the Universe boundarywhich restricted by radius 12{15 billions of light-years,it correspond to the theory of Universe expansion frommore its dense state in the past;

b) meshes in which walls the quasars are concen-trated not only change in size, but also that most im-portant, are deformed (are attened) as approachingto the Universe boundary that cardinally contradict tothe theory of the explosion for which is typical the ho-mogeneous expansion of a substance and, according-ly, proportional expansion of the sizes of the indicatedmeshes.

Thus, the second method of distances de�nition tothe quasars and theory of the dilating Universe, fromwhich this method follows, is necessary to consider er-roneous, not relevant to the laws of physics and theobserved phenomena of nature.

4. Estimation of local inhomogeneitiesin quasars allocation

The Delone triangulation is a set of lines pairing eachquasar with its nearest neighbouring quasars. Theselines not intersect and to form the delta circuits. Fromhere the name of the triangulation method was formed.

The Delone triangulation allows to determine alldistances between quasars in thin area of the Universe(i.e. practically on a plane). Further the statistical


Figure 4: Delone triangulation in the area 1

handling of multitude of these distances is carried outthat allows to obtain objective appraisal of large-scaleallocation of quasars in the Universe, and also to de-termine structure of the Universe as a whole. Afterthat the initial model of the Universe is con�rmed orrejected.

We shall show for example how the Delone trian-gulation method for area 1 was used. We shall remindthat about 380 quasars are in this area. Thus about 750distances between quasars is formed provided that thelines 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 verti-cal axis. Distance between the nearest quasars is putaside on a horizontal axis. The histogram shows thatthe distances rdNmax = 0:024R0 come across most fre-quently. Taking into account that R0 � 10�26 m, 1 ps= 3.1 �1016 m, this distance is equal about 77.4 Mps. Itpractically is equal to diameter of Universe honeycomb,which is estimated approximately in 50{100 Mps.

It is obvious, that on the obtained histogram thegreatest distances (more than 0.1{0.15 radiuses of gravi-tational interactions) should generally be excluded fromthe analysis, as they are interlinked with edge e�ects,i.e. that the isolated part of the Universe without thetaking into account of presence of neighboring quasarswas considered.

5. Discussion

The analysis of the received results has allowed to de-cide that:

I. The new method of distances de�nition (1) upto quasars does not contradict observed phenomena

Figure 5: Histogram of the interquasars distances

and common sense, quasars in cosmological gauges dis-tributed uniformly, and in smaller gauges form a foammesh structure of the Universe with the size of meshesabout 100 megaparsecs.

II. The old method of distances de�nition up toquasars gives the results, which contradict known stand-ings of the explosion theory and common sense. There-fore, concept of the Big bang of The Universe is alsountrue.

III. The accepted results of the astrophysicists areuntrue asserting that the quasars concentrate on par-ticular distances and are typical for a particular periodof the Universe life, as in their investigations the gen-eral dependence of quantitative density of quasars ondistance was considered, but their spatial distribution,inhomogeneity observation of sky both on corners, andon 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 Universewithout dependence from distances and angular stand-ing in space have averages of distribution, root-mean-square diversion and correlation factors, typical for auniform distribution of random quantities;

b) in smaller gauges the quasars are grouped in thinwalls of meshes (size about 50{100 Mps), reminding thelather;

c) the quasars allocation in meshes correlates withgalaxies allocation;

d) the Universe has no precise boundaries even ondistance in 30{40 billions light years;


e) asserting that the quasars concentrate on partic-ular distances and are typical for a particular period ofthe 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 repre-sentation about global structure and development dy-namics of the Universe as a single whole to con�rm theconcept of the stationary inconvertible Universe and toreject concept dynamic dilating Universe which erro-neously formed in the XXth century and taking the be-ginning from a so-called the Big Bang, which ostensiblyhas taken place of 12{15 billions years ago.

The discovery con�rms revealed earlier by one of theco-authors N.A. Zhuck the physical laws of the Universefunctioning and competence of their practical use forcognition of the world and practical needs of a man.

Appendix I

GENERAL INFORMATION ABOUTQUASARS

Investigations of the Universe through radio telescopeshave resulted in discovery such surprising objects asquasars. The increased resolving ability of radio tele-scopes has served as the background of quasars discov-ery. It has allowed de�ning the coordinates and angularsizes of objects emitting radio waves with more accura-cy than earlier.

Quasars discovery

Two 27-meter antennas of the California technology in-stitute which locate in Owens valley represented in pairwith each other the radio interferometer have beguncoordinates measurement of the radio emission sourceswhich have been recorded in the 3rd Cambridge cata-logue (3C) in 1960. The accuracy of coordinate deter-mination has reached �500 and as result measurementswas discovered that some sources have the very smallangular sizes.

September 26, 1960. T. Met'juz and A. Sandagehave photographed on a 200-inch telescope of the skyarea containing one of such sources 3C 48. Within arectangle of coordinates errors in this area there wereno objects except for the star 16m; 2V . Around the starthere were tracks of feeble nebula but the object lookedstar-shaped. October 22, 1960. A. Sandage has inves-tigated a spectrum of the discovered object, in whichthere was a strong combination of broad emission lines,which was impossible to identi�cate. Any of spectrallines was not possible to know in its spectrum, lineswas not possible to identify no with one chemical ele-ment. The color indexes 3C 48 were unusual too, they

corresponded to very hot objects with ultra-violet ex-cess.

By 1962 T. Met'juz and A. Sandage have identi�edwith star-shaped objects the radio emission sources 3C196 and 3C 286. 1963 became decisive, to this timeof K. Hazard, M. Makkej and A. SHimins with recordaccuracy determined the coordinates of radio emissionsource 3C 273. The object has appeared double withdistance between components in 1900 and diameter ofeach source less 1000 . One of source components coin-cided with "feeble star" (mV = 13m ). Young Dutch as-trophysicist Maarten Schmidt on observatory Mt. Palo-mar has investigated the spectrum 3C 273, in whichagain there were incomprehensible emission lines. Justhe has supposed that these lines can be identi�ed withthe Balmer hydrogen line if to admit redshift equal0.158.

The correctness of line identi�cation o�ered bySchmidt was proved by Dj. Ouk, which has foundin the infrared spectrum 3C 273 line H� in accuracyon that place where it should be with o�ered value ofredshift. After the speci�ed event T. Met'juz and Dj.Grinstejn identi�ed lines in the spectrum 3C 48 havingsupposed redshift z = 0:367.

Nine such objects became known to the end of yearand then the ow of discovery has gushed when becameclear on what attributes is possible them to search. By1967 was already found about 150 quasi-sidereal ra-dio emission sources (quasistellar sourse, QSS), in 1977them became 370 and very soon the name quasar (forsuch objects) was coined.

Basic observed properties of quasars

The quasars at observation through a telescope looklike as star-shaped objects, which besides are strongsources of radio emission. They have excess of radiationin ultra-violet and infrared area of a spectrum. Spec-trum contains broad lines of radiation, always stronglyshifted in the red side.

The quasars have a number of surprising properties:a) The power of their electromagnetic radiation is

extremely great from 1037 up to 1040 W. For compar-ison we shall specify that the power of radiation of ourGalaxy amount approximately 1037 W. It is supposed,that this high-power radiation can arise at a gravita-tional collapse of huge weight from 106 up to 1010 Solarweight;

b) The spectrum of radiated light �nds out strongredshift characterized in parameter z = ��/� , where� - wavelength of observation light, and �� - its red-shift in the side of long waves. This redshift is so greatthat, for example, the line � of series Lyman in a hy-drogen spectrum, at standard conditions observed inultra-violet area, appears in a visible part of a spec-trum;


c) The quasars change their brilliance, at some theoscillation frequency of brilliance reaches up to 3m andmore. For example, the quasar 3C 279 has the ampli-tude amount almost 7m and in a maximumof brillianceit is one of the brightest objects of the Universe, itsMB = �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 namedthem beautifully as \fuzz". So, in the center of such\fuzz" which is the size of a giant galaxy, a quasar likedense, tiny corn of a poplar in its shell is located.

The energy-release of quasars is huge. The luminos-ity of our Galaxy as was already mentioned amounts toabout 1037 W; the quasar luminosity on some ordersis higher. Total energy emitted by quasars is estimat-ed in 1054 watt-second. It is in 10 billions times morethan 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 ofluminosity occur in times by an irregular mode aboutone year and less (up to several days). Therefore, it ispossible to make a conclusion, that the sizes of quasarsdo not exceed a route transited by light during essentialchange of luminosity otherwise variability would not beobserved. Hence, it is indirectly possible to estimate thesizes of quasars, their diameters do not exceed one lightyear, i.e. the quasars are smaller even of single galaxies(For comparison the diameter of our Galaxy about 100thousand light years). From here follows that all thehuge energy of a quasar is generated in an insigni�cantsmall volume.

Starting from such observed quasars properties sev-eral guesses were made:

Either1) Or these objects located very much far outside a

Galaxy and luminosity of objects in 100 and more timeexceeds a luminosity of giant galaxy,

2) Or the quasars are objects thrown out from akern of a Galaxy with tracks of explosive activity ofkerns and moving with huge velocity, then distance upto 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 e�ect. Then the quasarsshould ee from us with huge velocity. Quite oftentherefore it is possible to meet in the literature theidenti�cation of the parameter z with the relativisticDoppler shift z =

p(1 + u/c)/(1� 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 eefrom 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 thequasars represent objects thrown out by kerns of galax-ies of a Local galactic congestion with almost velocity

of light removed from us no more than on 10 millionsa parsec (1 parsec = 3.26 light years = 3:1 � 1016 m),puts many new problems.

Today almost everyone recognizes that the shift ofquasar spectra in the side of long waves is explained notby Doppler e�ect, and it generates the cosmological red-shift. According to this explanation, the further fromus is located a quasar, the more its spectrum is shiftedin full conformity with cosmological e�ect of Hubble.

Cosmological models of the Universe

Any hypotheses and guesses explaining observed prop-erties of the Universe always are formulated on the ba-sis of de�nite cosmological model. Now in a cosmologythere are two main models. The �rst model is basedon a General Relativity (GR) and named as the mod-el of observed Einstein-Fridman Universe. The secondmodel was o�ered by such scientists as Bondy, T. Gold,F. Hoil and named as the model of the stationary Uni-verse.

In both models is recognized that the large-scalestructure of the Universe is identical everywhere andin all directions, i.e. the Universe is homogeneous andisotropic. But \the Perfect cosmological principle" thetheory of the stationary Universe says that, besides thatthe Universe is identical not only everywhere, but al-so always. In the theory of observed Einstein-FridmanUniverse there are solutions of two types. Accordingto �rst, the Universe is dynamic and is continuouslydilating after a so-called The Big Bang (the momentof the Universe birth). In the second version the ex-pansion slows down more and more, and then will bereplaced by squeeze and the Universe will be squeezedto a condition of extreme large density (condition of asingularity), and then again expansion will begin.

Today, the cosmological model of Einstein-Fridmanis traditional and universally recognized and all expla-nations of observed properties of the Universe are cre-ated, as a rule, on the basis of the speci�ed model.

Hypotheses about a quasars naturewithin the framework of conventionalcosmological model

Quasars as de�ned stage of the Universedevelopment

The statistical analysis of quasar redshift has shownthat the values z in general do not exceed de�ned val-ue z � 5:5 and shows the tendency to concentrate inan interval from z = 1 up to z = 3. In the beginningthis is explained that because of absorption of light ininterstellar gas the farther objects are inaccessible tomodern telescopes. However, later the other explana-


tion was put forward.According to it even with the help of more perfect

telescopes dilating horizons by the observed Universewhich allow to glance in its farther past, it is impossibleto discover new more remote quasars since before thede�ned moment they simply did not exist. And this mo-ment already now is within the reach of our telescopes.According to this cosmological interpretation since theradiation received by us from quasars today goes up tous about 10 billions years then the researchers observ-ing the quasars is looking in the past of the Universe on10 billions years back. The Universe then was at earlierstage of development and the processes taking place inits, di�ered by huge energies. It also explains unusualpower of quasar radiation.

Starting from such guess, it is possible to consider,that the quasars correspond to a de�ned phase of de-velopment of the Universe as a whole, and are a char-acteristic feature for its, far past. Accordingly, up toquasars existing on early phases of the Universe de-velopment there should be huge distances, which theobservations con�rm.

Con uence of galaxies as the reason of aquasars phenomenon

Observations and researches of the \fuzz" images aro-und quasars have resulted in new discovery. It is dis-covered that many of the \quasars" galaxies interactwith other galaxy. Percent of such pairs is rather highand it reaches 30 % in the systems with small redshift[11]. Such facts observed allow to suppose that phe-nomenon of a quasar in many cases can be aroused bythe galaxies interaction.

The speci�ed hypotheses are that the interaction ofgalaxies strongly perturbs motion of gas in a system,and it falls to the center of a galaxy. There, a super-massive black hole \gobble up" it and this process isaccompanied by liberation of huge quantity of energy,which we observe as a phenomenon of a quasar.

The modern researches show that the processes ofcon uence galaxies and the processes of activity ofgalactic kerns correlate among themselves. In this con-nection it is possible to suppose, that the epoch ofquasars formation can be simultaneously by epoch offormation of massive galaxies at the expense of mergingless massive units (dwarf galaxies). Straight observa-tions of master's galaxies (galaxies, which swallow upother galaxy) the nearest quasars through the Hubbletelescope have given con�rmation of straight connectionthe activity with interaction and con uence of galaxies.In particular, in case of master's galaxy of quasar PKS2349 is discovered that the satellite galaxy of a scaleBMO is immersed in its.

According to the above-stated the quasars repre-sent a rather complicated accretion system around asupermassive black hole located in the center of a mas-

ter's galaxy. It is so-called accretion disk and a shadeddisk or thick disk on which axis the radiolet is directedin case of radioloud objects, the system of fast yingclouds, which shape broad optical emission lines, andon large distances behind a disk give narrow opticalemission lines.

Similar \assembly" of galaxies is observed with thehelp of the Hubble telescope on redshift about 2{3.Such process can explain both as fast decrease of num-ber of quasars from the past to the present and well-known rupture in their distribution on large redshift.The radioloud quasars in model of con uence commu-nicate with the rotation of a black hole, which is initiat-ed or recent \strong" con uence of a comparable weightgalaxies or rather small quantity of "feeble" con uenceof a massive galaxy with dwarfs. Besides it is consid-ered, that the con uence lead to occurrence of activityof galactic kerns.

Quasars as a de�ned phase of a galaxy life

Many characteristics of quasars are observed and atgalaxies, i.e. between quasars and galaxies there isa continuous connection. Such galaxies reveal in thespectrum strong ultra-violet excess, some have appre-ciable 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 theywere named by N-galaxies.

The spectra of quasars are similar to spectra of kernsSeyfert galaxies that in the �eld of the kern have broademission lines indicating on the motion of large massof gas. The energy distribution in a spectrum is alsosimilar. The characteristics both radio emission andpolarization of quasars light and galaxies di�er fromeach other a little. The high-power ows of infrared ra-diation are observed both from quasars and from kernsSeyfert and radio galaxies. Therefore, hypotheses wereput forward that the quasars are active and superpowerkerns of remote, young galaxies.

Especially important and convincing evidence of na-ture unity of quasars and galaxies was the detection in1967 by Dj. Ouk of brilliance variability of a unob-structive radio galaxy 3C 371 with amplitude about2m . The brilliance variability of several N-galaxies andSeyfert galaxies soon also were discovered. It turnedout, that the brilliance variability is not a unique prop-erty of quasars, and this property is peculiar to galaxieswith an active kern.

The likeness of quasar properties with properties ofkerns Seyfert galaxies has given the basis to assumethat the quasars are kerns of young galaxies.

More late observations in the beginning of 70's andin 80's years of XX century have shown that the dis-covered feeble nebulas around quasars in color are sim-ilar to late blue spiral galaxies and sometimes are evenbluer. The blue color of galaxy indicates upon plenty


of young massive stars. It can mean that a nebula rep-resents a young galaxy in which there is a high-powerprocess of star formation.

In 1982 the American astronomers T. Boroson, Dj.Ouk, K. Grinss could found a good spectrum of nebulaaround quasar 3C 48 and have found in it, a narrow,typically stellar line of magnesium absorption. It wasthe �rst direct proof that the quasars are surroundedby stellar component and they are possibly consideredas kerns of born galaxies.

Conventional representations aboutquasars distribution in space

Detection chronology of new quasars, a ways oftheir search

Since the moment of discovery the quantity of the de-tected quasars is constantly increased. In process ofperfection of technical and methodological means ofsearch and identi�cation it is discovered more and morefar quasars. But if to analyse the detection chronologyof these objects then the next feature of quasars comesto light.

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

If to analyse technical ways of quasars detection,it is possible to see, that at �rst mainly the radi-oloud quasars are discovered then since 1965 radiosilentquasars are discovered. They are discovered as blue ob-jects, using the test of \ultra-violet excess". But suchtechnique of quasar detection becomes ine�cient at val-ues of redshift exceeding 2 and this fact could explainslowing down the rates of discovery of new quasars.

At the end of 80's of XX century new more e�ec-tive optical techniques of quasar detection have ap-peared. It has allowed in the �rst time, to discoverquasars with large value of redshift. But, despite oflarge-scale researches with application of modern testsof detection and identi�cation it was very di�cult to�nd quasars with redshift exceeding 5.5. The questionemerges whether it is possible to discover quasars withlarge value of redshift. Despite of limitations in mod-ern methods of detection the quasars in general shouldbe discovered at values z > 5:5. Such situation has re-sulted in the guess that on farther distances the quasarspractically do not meet. And density of a spatial distri-bution of quasars is fast incremented in range of valuesz �= 2� 3, and then is sharply reduced for large valuesof 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 onlythrough telescopes. The considerable interest for re-searches was represented the �xed coordinates of al-ready discovered quasars. The statistical researches ofquasar distribution in space in increase process of quan-tity of discovered quasars gave the more and more in-teresting results.

The researches of quasar distribution were carriedout on di�erent parameters including on value of red-shift z . Thus in general, histograms of distribution arebuilt, explored peaks in quasar distribution especiallynearby z = 1:95, but the further statistical analysis, asa rule, was not carried out.

The correlation analysis of a histogram of quasardistribution was carried out in 1971 by Carlsonn [9, 10],who has revealed qualitatively new feature of distribu-tion of quasars in space, the periodicity of distributionon argument ln (1 + z) . Calculation of an auto corre-lation function has con�rmed presence of the speci�edperiodicity. The sample of 166 objects was explored,and the period P on argument ln (1 + z) has made0.205.

Such fact, in a spatial distribution of quasars on red-shift required an explanation, and originally reason ofoccurrence such irregularity was seen in techniques ofquasars detection (e�ects of selection). But in the fur-ther the conclusion about strong in uence of e�ects ofselection was doubted and the objections against non-uniformity in distribution of quasars on ln (1 + z) wererejected.

The statistical researches of coordinates of discov-ered quasars were continued, the more and more newsamples, for a lot of objects were under construction,but the result remained the same, the redshift of dis-covered quasars tended to avoid some intervals z .

Today, the researches of periodicity in a spatial dis-


tribution of quasars are continued, but precise physicalinterpretations within the framework of conventionalcosmological model of the Universe have not obtained.

Conclusion

Any facts observed should be liable to careful under-standing and what obvious was this or that fact alwaysthere should be a de�ned shadow of doubt in the valid-ity of interpretation of this fact.

As it was possible to see, within the framework ofthe traditional cosmological model there are enough ofdi�culties and contradictions at interpretation of dis-covered properties of the actual world.

Appendix II

MODEL AND PHYSICAL LAWS OFTHE UNIVERSE

Introduction

The Universe is the study subject of cosmology. Cos-mology is the general part of mathematics, physics, as-tronomy and philosophy, which studies the structure,evolution, and physics laws of the Universe as a whole.

The integral notion about the Universe puts cosmol-ogy in a special position in relation to other sciences.Indeed, if any other science can study its subject fullyand comprehensively the investigator of the Universecan only examine part of the subject. Since the wholecan exhibit such characteristics which are not presentin its parts, the di�culties cosmology has been facingat all times can be understood.

The essence of the di�culties has always been asfollows: any physical theory could not fully explain theobserved properties of the Universe. If the theory wassomehow adjusted to describe some properties of theUniverse, the consequence that emerged did not agreewith other known features or fell outside the commonsense.

The situation is also aggravated by the fact that theMinkowski space-time in the General Relativity [2, 3],which represents the theoretical foundation of modernclassic cosmology, is described by ten variables, whilethe theory itself o�ers only six independent equations.Therefore, it is no wonder that no one could constructan objective pattern of the world yet based only on theequations of the General Relativity.

As a result of discrepancies in the theory, particularhypotheses needed to be advanced to explain certainproperties of the Universe. For this reason, many dif-ferent models of the Universe have appeared. Unfortu-nately, no one of them fully satis�es all the requirementsof the laws of logic or conforms to the real world.

At present, the o�cial science adheres to the com-monly accepted concept that the Universe appeared 12{15 billion years as a result of the Big Bang of the sub-stance, which had been in tremendously dense and hotstate. After that the substance expanded, cooled down,split into the matter and the electromagnetic �eld andformed galaxies, which are believed to continue movingfarther apart until now.

Such a model is based on the non-steady solutionsof the Einstein equations obtained by Soviet geophysicsand mathematician Fridman [4, 5] at the beginningof the 1920s and the concept of the exploding com-mencement in the dynamics of the Universe advancedby American physicist Gamov [6] at the end of the1940s.

The objective properties of the Universe, which al-legedly con�rm this model, are the discovery of the red-shift in the spectra of galaxies by American astronomerHubble [8] in 1929 and the Cosmic Microwave Back-ground Radiation at the temperature 2.7 K by Ameri-can radio astronomers Wilson and Penzias in 1965 [16].

The �rst discovery was interpreted by scientistsas the result of the motion of galaxies away from eachother and the second discovery was construed as the re-mainder (relic) of the electromagnetic radiation whichhad segregated from the initial substance and thencooled down to the said temperature during the expan-sion of the Universe.

The above-mentioned properties of the Universe, in-cidentally, are not the direct evidence of its expansion.For instance, the decrease in the frequency of lightcan be the result of either the expansion of the Uni-verse or the dissipation of the energy of light when itspread at great distances, while the osmic MicrowaveBackground Radiation can be either the remainder ofthe high-temperature explosion of the super dense sub-stance or the total radiation of all stars of the stationaryUniverse with the said dissipation of the energy of light.

The question about the model and the laws of theUniverse is comparable with a problem of what is prime:an egg or a hen. So if we de�ne cosmology as the sci-ence about the Universe, we are immediately facing theproblem of what is initial: the model of the Universefrom which the law of physics of the Universe follow,or the laws of physics of the Universe, on the basis ofwhich the model of the Universe is constructed?

Apparently, the problem does not need a direct an-swer. However, a third question, which is as if a quasi-superstructure over the dilemma about the primacy ofthe model or the laws of the Universe, requires resolv-ing. The point is about the proportion and interrelationof such philosophical categories as the \whole" and the\part" and also the philosophical law of quantitativechanges passing into qualitative changes. Here again,strictly parallel movement is needed.

To study the whole by its part, it is important tohave continuous integration of notions on the subject of


Figure II.1: Systems of readout

the investigation from di�erent points of view at everystage of its investigation and continuous coordination ofoutcomes of the theory under development with the ob-jective reality. Non-observance of the principle of con-formity, occurrence of internal contradictions, singular-ities and paradoxes while applying the given theory forthe description of the whole indicates to the falsity ofthe way taken by the investigators. It is the very situ-ation, which has developed in cosmology nowadays, itso�cial theoretic ground being based on the idea of BigBang.

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 ofrather propellent objects.

Correctly to answer this problem, we shall considertwo inertial systems of readout K , K0 and bound withthem two rulers, as it is shown in a Fig. II.1.

Let at that moment, when the beginnings of rulers qand q0 coincide with each other, the bulb in a point q ,bound with a �xed ruler, will light up. In time t lightwill reach a point S on this ruler. For the same time therelative frame ruler will move and on the contrary pointS there will be a point S0 . Thus distance, which lighthas passed along a relative frame ruler on quantity vtwill be less than distance which it has passed on a �xedruler. Hence, observer who is taking place in a pointS (that is in �xed system of readout) on the gauges ofspace and time should make a deduction, that the frontof a light wave catches up a point S0 along a propellentruler with velocity c0 = c � v . At a motion in theopposite direction will be received c0 = c+ v .

All above-stated does not contradict a postulate ofa special theory of relativity, as the speed of light isconstant only in inertial systems of readout, and c0 -is a speed of light in one inertial system of readoutmeasured on gauges of space and time of other inertialsystem of readout. Let's term it as a local velocity oflight.

Thus, from this point of view the local velocity oflight represents a tensor of the second rank (naturally,

Figure II.2: The tensor of light speed

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

The gravitation law

As it is known, Einstein has o�ered two views of theequations of the General Theory of Relativity whichdi�er from each other on an addend with the cosmolog-ical term � :

Rik � 1

2Rgik = ��Tik; (II.1)

Rik � 1

2Rgik � �gik = ��Tik; (II.2)

where Rik is the Ricci tensor, convolution of the Riman-Cristo�el curvature tensorm Rl

ijk ; Tik is the energy-momentum tensor of a substance without a substanceof gravitational �eld; gik is the metric tensor of four-dimension spacetime; R is the curvature scalar, con-volution of the Ricci tensor; � = 8�G=c4 is Einstein'sconstant; c is the light speed; G is Newton's gravita-tional constant; i; j; k; l = 1; 2; 3; 4.

For a unique select of the equations it is neces-sary to take into account some performance of the Uni-verse. Such performance is global atness of the Uni-verse which mathematical expression is equality

Rlijk = Rik = R = 0: (II.3)

As for the actual Universe �lled with substance withde 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 featuredonly with the equations (II.2). And, the diversions from at space-time under activity of material masses can be


presented precisely (precisely!) only in a composition ofthe total which corresponds to the assignment of a ten-sor gravitational �eld hik on a background of the atmaterial 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 to zero of a covariant derivative(derivative) of ten-sor density

p�ggik and corollaries of this equality (inLorentz's coordinates):

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

where the point with comma designates a covariantderivative, and the comma is usual derivative.

After that the equations (II.2) with the help oftransformation (II.4) and requirement (II.5) are givenin the �eld equations of the General Theory of Relativ-ity

2hik � 2

3�hik = 2�T 0ik; (II.6)

where T 0ik is an energy-momentum tensor of a sub-stance together with a substance of gravitational �eldwhich is oozed from the left-hand part of the Einstein'sequations. Under the same requirements in [1, 4] theidentity of Lagrangians for a deduction (II.2) and (II.6)is proved also.

Taking into account homogeneity and isotropy ofthe Universe (that is symmetry of a problem), for aspherical-symmetrical material body of mass m theequations (II.6) give the exterior solution as Yukawapotential

' = �Gmre�

r

R0 : (II.7)

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

R0 = c0r

3

4�G�0: (II.8)

For two of material bodies with masses m1 and m2

the following law of gravitation is gained

F = Gm1m2

r2e�

r

R0

�1 +

r

R0

�: (II.9)

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

Identity of inertial and gravitationalmasses

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

F � Gm1m2

r2

�1� r2

R20

�; (II.10)

which shows, that all material bodies in the Universeinterreact with each other practically only in limits ofradius of gravitational interactions equal approximately1026 m (or 20 billions of light years).

On the other hand, if to compare an actual law ofgravitation and law of gravitation of Newton, it appearsthat the area under a curve of force of the actual law onan interval from 0 up to 1 is precisely equal the areasunder a curve of the law of gravitation of Newton onan interval from 0 up to R0 . Hence, law of gravitation(II.9) valid for the actual Universe, from the energypoint of view by the law of Newton gravitation canbe replaced restricting radius of activity of forces byquantity R0 . The given approach allows to decide aseries of remarkable problems promptly and obviously.

In view of above-stated we shall analyse, how thearea of interaction of a material point of mass m withthe Universe will vary at its dispersal up to velocityv and in what all this will give. It is to show that thenew area of interaction of a point with medium also willrepresent a ball of radius R0 , but moved forward on acourse of its motion on quantity r (as in expression forR0 it is necessary to substitute c0 ). It is possible alsoto show that the relation is valid

r =v

cR0; (II.11)

Thus, the area of interaction of a propellent masspoint displaces forward on a course of a motion propor-tionally velocities of its motion. In a limit, that is whenthe velocity of a motion is equal to speed of light thepropellent point should be on a surface of its area ofinteractions. But it just and probably only for light.

At dispersal the point m loses gravitational con-nection with a part of space u behind of itself and willenter gravitational connection with a part of space wahead of itself (Fig. II.3). The sizes of the areas bothare identical and depend only on velocity v , but the sit-uation of a point m concerning them is unsymmetrical.Hence, the aggregate operation on overcoming forces ofa gravitation of area u and forces of a gravitation ofarea w is not equal to zero.

The author managed to �nd receptions of de�nitionof this operation. If to take into account a probableinitial velocity v0 a material point, for low speeds theoperation has appeared to equal quantity

A =mv2

2� mv20

2: (II.12)


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

Thus, we have received, known from mechanics thetheorem, of change of a kinetic energy of a body. If theobtained expression to di�erentiate on velocity and ontime, the second Newton's law will be received. All thisis valid in a relativistic case.

Charakteristic feature of the obtained results is thatboth in the theorem of change of a kinetic energy, andin the second Newton's law not inertial, but gravita-tional mass enters so long as only such mass consideredfrom the very beginning. So the identity of inertial andgravitational masses spirit of the Mach's principle [15]is proved and the mechanism of interaction of materialbodies with the Universe is uncovered.

Gravitational viscosity and geodeticcurvature of the Universe

After dispersal (cancellation of local force) of materialbody along coordinate X its free motion is featured bythe equation

d2X

dt2+H

dX

dt= 0; H =

r4�G�0

3; (II.13)

where H is the Hubble's constant, which has absolutelyother physical sense, as it is accepted in a conventionalcosmology.

By presence of the second (dissipative) addend thenew law of a free motion di�ers from the �rst Newton'slaw. As a whole one of the most prime statements ofthis law can be such: if the local forces do not act ona body, the standing of its interaction area from theUniverse (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 grav-itational viscosity. As the stationary value of Hubblehas the order 10�18 s�1 , the gravitational viscositypractically has no an e�ect for local processes (for ex-ample, in gauges of Solar system). In a distance equal

to half of medial distance between galaxies the forces ofthe gravitational viscosity become comparable with thecentrifugal forces and answer for shaping of the medial-gauge structure of the Universe, that is for shaping ofgalaxies.

The concept of the gravitational viscosity of theUniverse adjoins by a tight fashion to the conceptsof a�nities (parallel transport of vector) in a non-Euclidean geometry of multivariate spaces. For a mo-tion of the nonconservative systems | that is in thegeneral view | there is a relation for the curvature ofspace

Kj (t) =d2Xj

dt2+ �jlk

dXl

dt� dX

k

dt= ' (t)

dXj

dt: (II.14)

The medial addend with Christo�el's �gures of the�rst kind (a�ne compendency) �jlk indicates a degreeof normal curvature of space (we shall term it as geo-metrical) in which the parallel transport of vector andthe letter on change of the length of the vector, thatis on the existence of a dissipation of energy. It deter-mines so-called geodetic curvature of space

K =qgijKi (t)Kj (t): (II.15)

For the actual Universe the geodetic curvature isequal

K = K0

r1� v2

c2; (II.16)

where K0 = Hc is constant for the Universe coe�cientequal approximately 10�10 m/s2 .

In the whole the analysis of all the results shows thatthe motion concerning the Universe has a character ofa terrain clearance motion, but on activity of the localphysical laws it cannot be noted (except for inertia andred bias in spectrums of radiation of other galaxies).

The propagation law of light and theHubble's diagram

The analysis of interaction of light with the Universehas shown that gravitational potential (�c2 ) acts on it,giving power loss and, as a corollary, change frequency� in relation to initial �0 under the law.

� = �0e�

r

R0 : (II.17)

The given law completely permits photometer para-dox, explains a nature of red bias in spectrums of ra-diation of other galaxies without engaging a Dopplere�ect and gives a new formula of de�nition of distancesup to galaxies

L = R0 ln (1 + z) ; (II.18)


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 Hubble's diagram) gains a view:

m = 5 lg�p

1 + z ln (1 + z)+ 21:68: (II.19)

In a gamut of apparent values of stellar magnitudesthe given dependence practically is linear and complete-ly coincides experimental datas.

The law (II.17) completely explains a nature, nu-merical performances and character of allocation ofbackground microwave radiation. Actually, it is not arelic of the Big Bang, and aggregate radiation of allradiants of electromagnetic radiation (stars, galaxiesetc.) of the Universe. If to integrate the whole ra-diation impinging on a single site on space from zeroto in�nitum the temperature of this radiation will bedetermined by the formula

T0 =4

rLs�0R0

4�Ms; (II.20)

where Ms; Ls is medial mass and complete radiation ow of a medial star (or galaxy); � is the Stefan-Boltzmann constant.

The evaluations show, that temperature of integrat-ed radiation is equal to several degrees above terrainclearance zero (more precisely to calculate it is impos-sible), as it is observed actually. And its spectrum cor-responds to a radiation spectrum of an absolute blackbody.

Large-scale structure of the Universe

The actual law of gravitation has a series of pleasantfeatures. So, the evaluation of a binding energy of amaterial body of mass m from the Universe gives quan-tity

E0 = �mc2; (II.21)

which is equal precision to an internal energy of a bodytaken with an inverse. In contrast to it, the law ofNewton gravitation gives a minus perpetuity. That iswhy with application of a Newton's laws to the in�niteUniverse the gravitational paradox also has appeared.In the actual Universe with the actual law of gravitationsuch paradox does not exist, and the mass appears ameasure of connection of the given material body withthe whole Universe.

The actual law of gravitation gives one more impor-tant corollary: with mass shown in interactions with amaterial body depends on a relation of radius of a bodyR to radius of gravitational interactions R0

M =R2c2

2GR0

0B@1� e

�

2R

R0

1CA : (II.22)

At R� R0 the mass of a body is proportional to itsvolume, and at R� R0 (or that is the same when R!+1) to surface area of a body. It gives in a deductionabout ability of a substance to create screen e�ect. Itis capable to explain virial paradox and existence ofgravitational-makes of areas of the Universe.

The interesting physical sense has also radius ofgravitational interactions (II.8). It appears that it cor-responds in precision to radius of a black hole on whichsurface the speed of light is equal to the �rst solar es-cape velocity. Thus, it is possible to tell that we live atin the centre of a black hole, but it is not our privilege,and the property of the Universe to form around of anypoint gravitational-makes area. By the way accelera-tion due to gravity on a surface of such black hole isequal only 10�10 m/s2 .

On the other hand, if to unit two identical materialobjects in one, not changing density the mass of theobtained object shown in interactions will be less thantotal masses of builders. It also should be expected, asthe formally given law is similar to the law of nuclearinteractions in the �eld theory of nuclear forces.

In classical physics there is a special theorem prov-ing that inside a spherical-symmetrical material shellthe gravitational �eld misses or, more precisely, thatresultant of force, all the gravitational forces is equalto zero. Using of the actual law of gravitation it hasappeared that the closer point is to a shell the strongerit is attracted to it. Di�erently, any spontaneous obtu-rating of a material medium of the Universe as a shellconducts to the further shaping of such shell. That iswhy the Universe has cellular structure in major gaugeswhere the aggregations of galaxies are in thin walls ofthese meshes and superaggregation and on crosses ofmeshes.

It is necessary to note, that in 1971 Karlsson hasfound out for the �rst time a cyclic change of a spec-tral radiant density of quasars proportional argumentln (1 + z) , where z is red bias of their spectrums. Suchallocation of quasars correlates with allocation of galax-ies forming in the Universe homogeneous thin-walledaggregations as meshes.

In view of the formula (II.18) cyclic changes of aspectral radiant density of quasars are conversed tocyclic dependence of allocation of quasars on distancesindicating homogeneity of the Universe not only inspace, but also in time, that is on its stationarity forthe last a minimum of 40 billions years (so much timethe electromagnetic waves went to us from the farthestquasars).

Thus, the author has designed the new stationarymodel of the Universe which approximately on 40 pa-rameters is compounded with the properties of the ac-tual Universe and has the same right on existence aswell as model of Big Bang.


Appendix III

THE FIRST DEDUCTION OF THEPROPAGATION LAW OF LIGHT

From the regularities of the interaction of moving ob-jects with the substance of the Universe, which havebeen considered in Appendix II, the conclusion is drawnthat the gravitational potential should permanently acton a moving photon, i.e., quantum of light. Let us de-termine the said potential

�0 = �GM0

R0= �G4�R

30�0

3R0= �4�G�0R

20

3=

=

��R0 = c

r3

4�G�0

�� = �c2: (III.1)

The result obtained is evidence of a lack of in�nitegravitational potentials in a homogeneous and isotropicspace. It is in this way that a so-called gravitationparadox 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 ofthe range of gravitational interaction is determined byexpression

g0 = �Hc; (III.2)

in which abbreviation

H =

r4�G�0

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 theequality

h� =h�

c2g0dr + h�

0

; (III.6)

where �; �0

are frequencies of light before and afterthe light has passed the distance dr . Planck's constantcancels 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 �nallyobtain

d�

dr+

1

R0� = 0: (III.8)

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

� = �0 e�

r

R0 : (III.9)

As a �rst approximation expression (III.9) becomes

� = �0

�1� r

R0

�(III.10)

or in other presentation

� � �0�0

= �Hcr: (III.11)

Considering the Doppler e�ect for the source andthe receiver of light, which move away one from theother

� � �0�0

= �vc; (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 ap-proximation the law of propagation of light can be easi-ly confused the Doppler e�ect. This was the case whenthe redshift in the radiation spectra of outlying galax-ies was interpreted as the galaxies bouncing apart, i.e.,the universal extension of the Universe. It was no won-der (though also revolutionary), as the Doppler e�ecthad been studied very well and the properties of theUniverse as a nonconservative system did not followfrom anywhere. Note that the general relativity in itsconventional formulation rules out this property of thenonconservative Universe.

The law of propagation of light (III.9) is yet moreevidence that the Universe does not expand at all andthat the light, when spreading in the space, loses itsenergy since the light is permanently forced to breakaway from gravitating masses behind.

The numerical value of Hubble's constant is approx-imately equal to 1.67 �10�18 s�1 , which corresponds tothe equivalent speed of 51.6 km/s �Mps of the extensionof the Universe.

Presently, the redshift in the spectra of galaxiesserves as an instrument to calculate the distance to thegalaxies. For this purpose the variable z is used whichis expressed via the wavelength of light

z =�� 0�0

; (III.14)


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

and the calculated formula [55]

r1 =(1 + z)2 � 1

(1 + z)2 + 1� cH: (III.15)

If we utilize the deduced law of propagation of light(III.9), we reveal that the calculated formula should bequite di�erent

r = R0 ln (1 + z) : (III.16)

In Fig. III.1 diagrams of distances to galaxies arepresented: the dash curve r1 corresponds to calcula-tions by formula (III.15); the solid curve r correspondsto calculations by formula (III.16); the dotted curve ershows 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 deter-mining the distance to a galaxy by the convention-al method, errors become conspicuous starting fromz = 1. When z arrives at 5...6 the value of the er-ror reaches the magnitude of the measurable parameteritself, i.e., the distance. This leads to errors in the de-scription of the general pattern of the world, though thepremises to doubts the correctness of formula (III.15)have existed for a long time.

Appendix IV

THE SECOND DEDUCTION OF THEPROPAGATION LAW OF LIGHT

The unrestricted motion equation of material body inthe 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 evaluatethrough the gravitation constant G and the averagedensity of the Universe �0 by formula

H =

r4�G�0

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 about10�69 kg.

Considering, that the equation (IV.1) is valid formaterial body of any nature we apply it for descriptionof motion these particles. On the other hand, taking in-to account a polarizability of an ether, i.e. the presencein it of elastic properties (that is been con�rmed byspread of wavelike processes as electromagnetic waves)in the obtained equation it is necessary to add one moreitem �!20X named the recovery force (here !0 is theether particles oscillations eigenfrequency). As a resultthe motion equation will be obtained

�d2X

dt2+ �H

dX

dt+ �!20X = 0; (IV.3)

where X is a shift of ether particle at any moment oftime.

As the mass of ether particle is been a member ofall items of the obtained equation then it is possible toexclude its and to simplify the equation to a view

d2X

dt2+H

dX

dt+ !20X = 0: (IV.4)

The equation (IV.4) is a desired equation of etherparticles motion. We shall search its solution in theform of

X = e�

t

2� cos (!t + ') ; (IV.5)

where � , ! and ' are unknown quantities. By directsubstitution is determined that (IV.5) is a solution ofthe equation (IV.4) for any ' provided that

� =1

H; (IV.6)

!2 = !20 �H2

4: (IV.7)

The most common solution of the equation (IV.4)is a superposition of two linearly independent solutionswith two initial conditions for shift X (0) = X0 andvelocity (dX=dt)0 = _X (0) = _X0 of ether particles byt = 0. For example, we shall take ' = 0 and ' =��=2. Then common solution of the indicated equationis possible to present as

X = e�

Ht

2 (C1 sin!t + C2 cos!t) ; (IV.8)


where C1 and C2 are integration constants. For theirde�nition at �rst we shall determine derivative of ex-pression (IV.8)

dX

dt= e

�

Ht

2 (C1! cos !t �C2! sin!t)�

�H2e�

Ht

2 (C1 sin!t+ C2 cos!t) : (IV.9)

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

C1 =1

!

�_X0 +

H

2X0

�; (IV.10)

C2 = X0: (IV.11)

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

X = e�

Ht

2�1

!

�_X0 +

H

2X0

�sin!t +X0 cos !t

�:(IV.12)

For feeble attenuation (and it is real so, as H �10�18 s�1 is negligible quantity) exponential factorexp (�Ht=2) is possible to consider as stationary valueduring one cycle of oscillations. Under such conditionsit is possible to neglect an augend in (IV.9) and easilyto show, that the total energy of a particle E (the sumboth kinetic and potential) is equal

E =� _X2

2+�!20X

2

2= E0 e

�Ht; (IV.13)

where the initial value of particle energy E0 is deter-mined by expression

E0 =�

4

�!2 + !20

� �C21 +C2

2

�: (IV.14)

As in a microworld there is a quantization of energyproportionally by Plank constant h , the energies E andE0 will be proportional to frequencies � and �0 by theformulas

E = h�; (IV.15)

E0 = h�0: (IV.16)

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

� = �0 e�Ht: (IV.17)

Being aware of Ref. [28] that the Hubble constantH is bound to radius of gravitational interactions R0

by dependence (c is velocity of light)

H =c

R0; R0 = c

r3

4�G�0; (IV.18)

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

� = �0 e�

r

R0 : (IV.19)

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

r = R0 ln (1 + z) ; (IV.20)

where

z =� � �0�0

(IV.21)

is a redshift of their radiation spectrums.The law (IV.19) have been completely proved by

observations [28]:| by real presence of redshift in radiation spec-

trums of galaxies and quasars;| by the missing of bright luminescence of the sky

at night (contrary to a known photometer paradox ofclassical physics);

| by presence of microwave background radiationof space which is aggregate radiation of all stars of theUniverse with taking into account the law (IV.19);

| by Hubble diagram which in a linear part coin-cides with the diagram obtained on the basis of the law(IV.19);

| by allocation of galaxies and quasars in space ofthe Universe (this discovery is still developed).

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-it�atstheorie. Ann. Phys., 49, 769{822 (1916).

[4] Friedmann A. \�Uber die Kr�ummung des Raumes."Ztschr. Phys., 10, 377{386 (1922).

[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 The-ory of the (Einstein) Gravitational Field in an Arbi-trary Backgraund Space-Time." Comm. Math. Phys.,94, 379{395 (1984).

[8] Hubble E. \A relation between distance and radial ve-locity among extra-galactic nebulae." Proc. NAS, 15,168 (1929).

[9] Karlsson K.G. \Possible discretization of quasar red-shift," Astron. and Astrophys., 13, 333, (1971).


[10] Khodjachich M.F. \Csmological periodicities in ra-diospectrums of quasars," Spacetime & Substance, 1,3, 120 (2000) (in Russian).

[11] Kontorovich V.M., Krivitsky D.S., Kats A.V. \Explo-sive"evolution of galaxies (an analog of collaps) andappearance of quasars in the merger model." PhysicaD 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 andNucleas. 17, 1{153 (1986).

[14] Logunov A.A., Mestvirishvili M.A. \The RelativisticTheory 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." SeventeenthTexas Symposium on Relativistic Astrophysics andCocmolody. Annals of the New York Academy of Sci-ences, 759, 87 (1995).

[18] Zhuck N.A. \On the some results following from theuniversal gravity law." Borisoglebsk, 1986, 58 pp. (inRussian).

[19] Zhuck N.A. \Metamorphoses of cosmology." In \TheRelativity Theory: for and against," FENID, Gomel,3, 89 (1991) (in Russian).

[20] Zhuck N.A. \The cosmological solutions of the Einsteinequations." Kharkiv, KhVVAUL, 1995, 16 pp. (in Rus-sian).

[21] Zhuck N.A. \New overviews about the Universe andits laws." The 1-st RTI TTR scienti�c conference, RTITTR, Kharkiv, 1998, 5{14 (in Russian).

[22] Zhuck N.A. \The cosmological solutions of the Einsteinequations," Ky��v, Author's Certi�cate of series PA, No1718 with a priority of January 28, 1999 (in Russian).

[23] Zhuck N.A. \The new stationary model of the Uni-verse." The Gamov memorial international conference\The Univerce of Gamov: original ideas in astrophysicsand cosmology" (GMIC'99), Odessa, August 16{22,1999, Abstracs, p. 37.

[24] Zhuck N.A. \Cosmic equilibrium electromagnetic radi-ation," Kharkiv Univ. Public., 456/2, 2000, p. 244 (inRussian).

[25] Zhuck N.A. \The Microwave Background Radiation asaggregate radiation of all stars." The XVII internation-al conference \Actual problems of extragalactic astron-omy," Puschino, Moscow region, Russia, April 12{14,2000 (in Russian).

[26] Zhuck N.A. \The axiomatic theory of the MicrowaveBackground Radiation." The Joint European and Na-tional Astronomical Meeting \European Astronomy atthe 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 gravitation-al masses." The Joint European and National Astro-nomical Meeting \European Astronomy at the Turnof the Millennium" (JENAM-2000), Moskow, Russia,May 29 { June 3, 2000, Abstracs, p. 168.

[28] Zhuck N.A. \Cosmology," Kharkiv, Model VselennoyLtd, 2000, 464 pp. (in Russian).

[29] Zhuck N.A. \Field formulation of the General Rel-ativity and cosmology." The Ukrainian-Russian con-ference \Gravitation, cosmology and relativistic astro-physics" (GRAV{2000), Kharkiv, Ukraine, November8{11, 2000, Abstracs, p. 37.

[30] Zhuck N.A. \Cosmological e�ects in bulky Michelson-Morley interferometers." The Ukrainian-Russian con-ference \Gravitation, cosmology and relativistic astro-physics" (GRAV{2000), Kharkiv, Ukraine, November8{11, 2000, Abstracts, p. 73.

[31] Zhuck N.A. \The identity of inertial and gravitationalmasses is proved!" Spacetime & Substance, 1, 1, 23{28(2000). http://spacetime.narod.ru.

[32] Zhuck N.A. \The Microwave Background Radiation asaggregate radiation of all stars."Spacetime & Substance, 1, 1, 29{34 (2000).http://spacetime.narod.ru.

[33] Zhuck N.A. \Gravitation viscosity and geotetic curva-ture of the Universe." Spacetime &Substance, 1, 2, 71{77 (2000). http://spacetime.narod.ru.

[34] Zhuck N.A. \Gravitation viscosity and geotetic curva-ture 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 Relativi-ty and cosmology." Spacetime &Substance, 1, 4, 71{77(2000). http://spacetime.narod.ru.

[36] Zhuck N.A. \Cosmological e�ects in bulky Michelson-Morley interferometers." Spacetime & Substance, 1, 5,71{77 (2000). http://spacetime.narod.ru (in Russian).

[37] Zhuck N.A. \Field formulation of the General Relativi-ty and problems of cosmology." Spacetime&Substance,2, 1, 71{77 (2001). http://spacetime.narod.ru.

[38] Zhuck N.A. \The Cosmos Microwave Background Ra-diation as aggregate radiation of all stars." Physics ofConsciousness and Life, Cosmology and Astrophysics,1, (2001). (In Russian).

[39] Zhuck N.A. \Properties of the Yukawa poten-tial 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] Databaseon 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.


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 thenature, as Aether is executed in eight millimeter radiowaves range. The ethereal wind speed and this speed verticalgradient near the Eath's surface have been measured. The systematic measurement results do not contradict theinitial 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 channelphase characteristic of 8-mm range radiowaves prop-agation have revealed the problems, connected withits model elaboration [1{4]. The model [3] describedthe possible spatial e�ects in uence, but this idea hasnot been developed further due to the quantitativedivergence between demanded and measured atmo-sphere parameters. The interference model [4], as awhole, explained the observed e�ects, but in some cas-es the qualitative divergence between the calculationand measurement results took place. The further prob-lem analysis has shown that the hypothesis engagingof the radiowaves propagation medium anisotropy hasenabled to give the calculation results in conformitywith the measurement results. It was supposed thatthe anisotropy is stipulated by the directional medi-um motion of radiowaves propagation and this medium ow has the space origin. Some information aboutsuch medium motion parameters was taken from thepapers [5{7]. The works [5, 6] have been executed inorder to the hypothesis experimental check about theAether existence in the nature as the material medi-um, which �lls the Global space and is the buildingstu� of all kinds of matter, the motions of which arerevealed like physical �elds and interactions. In duecourse 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 aboutthe existence of such material medium, as Aether, inthe nature wasn't accepted. We'll consider the majorwork results, which were executed in this direction tak-

1e-mail: [email protected]; Ph.: +38 (0572) 448742

ing into consideration the long-life and signi�cance ofthe problem. We'll try to determine the reasons, whichhave made the physicists of that time consider the workresults [5, 6] as error and refuse the Aether concept.

In 1877 D.K. Maxwell noticed, that while the Earthmotion through Aether there should be an etherealwind on the surface, which changes the light speed dis-tributing in Aether. It is known that A.A. Michelsontried to �nd out an ethereal wind in 1881 for the �rsttime [8, 7]. With the help of a cross shaped interfer-ometer with the length of the optical path about 2.4m, within the hypothesis of �xed Aether, he expectedto receive the bands displacement of an interferencepattern, conforming the orbital motion speed of theEarth by the value 30 km/s. However the measureddisplacement, which corresponded the speed by thevalue only 3{4 km/s. Michelson related this result tomeasurement errors and concluded about the initialhypothesis inaccuracy of stationary Aether. However,it is considered in physics almost since that time, that\Michelson experience" has shown in general the in-accuracy imagination about such medium existence asAether in the nature. Many explorers didn't agree withsuch matters. The attempts to �nd out this mediumcontinued, including Michelson himself.

In 1925 D.K. Miller received the optical path of thelength about 64 m with a cross-shaped interferometer,as a result of long systematic measurements, that thesuspected ethereal wind speed at the altitude 265 mabove the sea level (Clevelend) has the value about 3km/s, and at the altitude 1830 m (observatory MountWilson, Pasadena) is about 10 km/s. The motion apexcoordinates of the Solar system were determined: thedirect ascension 17:5h , declination +650 [5].

212 Yu.M. Galaev

The Miller works have attracted the great physi-cists' attention. The discussion has started about them,in which the in uence of possible unaccounted factorson an optical interferometer was discussed �rst of all. Inthe work [10] S.I. Vavilov expressed, perhaps, the com-mon opinion formed: \...the Miller's interferometer is sosensitive, that many local in uences, considered hard,can be the cause of systematic bands displacement".Here again: \In any case, the experiments repetitionin the other place and by the other device is neces-sary at this situation." It was clear, that the interfer-ometer is required to save the environment parametersfrom the change a�ect. The solution seemed apparent -the interferometer should be placed into the thermostatand then into the pressurized chamber together withthe thermostat. So it happened, but all the attemptsin order to repeat Miller's experiment, except the ex-periment [11], were performed by the devices, whichwere placed in metallic chambers. R.D. Kenedy [12,7] increased the interferometer sensitivity. The devicewas placed in the pressurized metallic chamber. Themeasurements were conducted at the same altitudes,as in [5]. The bands displacement was not observed.K.K. Illingwort [13, 7] improved Kennedy's device, butalso these measurements showed a zero result. E. Stael[14, 7] placed an interferometer in the metallic cham-ber, i.e. thermostat, and raised it in an air balloonup to the altitude 2500 m. The required e�ect wasnot 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 dis-placement of an interference pattern value no more than1/50 of the expected e�ect was measured with the in-terferometer having the optical path length about 26m, connected with the solar System motion having thespeed 300 km/s. In other words, the speed of relativemotion of the value 6 km/s was measured. The interfer-ometer has been placed into a fundamental building ofthe observatory optical workshop for work temperatureregime stabilization. The pressurized metallic chamberwas not applied. Unfortunately, the problems, whichthe authors overcame at the experiment execution, werelisted in general in this extremely laconic work (1 page).The measured results are presented only in such kindas they were given in the above mentioned work.

The experiment by G. Yoosa 1930 [15] was the lastexperiment on the ethereal wind detection, which wasexecuted with an optical interferometer. The devicewas made on the quartz basis by the corporation Tseys,it was hanged in the vacuum-metallic chamber and sup-plied with photographic registration. The measurementresults showed that the required ethereal wind, in anycase, does not exceed the value 1 km/s (the deviceresolving capacity). Miller's measurements should beconsidered �nally as the error ones and stipulated byoutside causes after zero work result [15].

In 1933, Miller has marked the shielding property

of metal covers in his work [6]. However the scienti�ccommunity did not react properly to such peculiarity,shown by him in this work, as, perhaps, the positivework results [11], as there was a lot of experiments withzero results obtained with the interferometers, screenedby metallic chambers by that time. The physical shield-ing phenomenon interpretation was given by V.A. At-sukovsky [16] for the �rst time, having explained it bythe fact, that the electrons in metals will create so-called \Fermi's surface".

After 1930 Michelson-Miller's experiment ceased totake a central place in physics. Only in 50 years, therewas a capability of the experiment realization, whichdidn't repeat Michelson's scheme, but being its ana-logues in the results interpretation sense after the de-vices appearance, based on completely other ideas (res-onators, masers, Mossbauer e�ect etc.). Such experi-ments were conducted [17{20]. And again, the commontool error of these experiments was the usage of ethe-real wind e�ects detection of di�erent metallic cham-bers. They were metallic resonators in [17, 18, 20], leadchamber in [19], since it was necessary to work with agamma-radiation. The works' authors, perhaps, havenot given the proper signi�cance to Miller's conclusions1933 [6] about the inapplicability of metal boxes in theexperiments with an ethereal wind.

Thus, proper checks of Miller's experiments weren'tconducted yet until nowadays, in spite of numerousphysicists' attempts to repeat his experiments! Allhis followers carefully screened the devices from anethereal wind by metal chambers, and, according toA.A.Atsukovsky's image expression, \...it's the samethat to make the attempts to measure the wind, whichblows outdoors, looking on the anemometer put in adensely close room" ([7], p. 4). The known works un-til nowadays cannot be ranked as experiments, whichcould con�rm or deny Miller's results, con�rm or denythe hypothesis about Aether existence in the nature.The measuring means, unsuitable for ethereal winde�ects measurement, were applied in all these works.

The great job for work collecting and analysis, ded-icated the ethereal wind problem, was performed byAtsukovsky [7]. The aether model is o�ered and theaether dynamic picture of the world was designed inhis works [21, 22, 16]. The Aether is represented asa material medium, which �lls in the global space andhas the properties of viscous and compressible gas, itis a building stu� for all material formations. The el-ement of Aether is an amer. The physical �elds repre-sent di�erent forms of Aether motion, i.e. the Aether isa material medium of electromagnetic waves propaga-tion. The gradient boundary layer is formed at mutualmotion of the Solar System and Aether near the Earthsurface, in which the Aether running speed (etherealwind) increases with an altitude. The ethereal windapex is northern. It is shown, that the metals have larg-er aether dynamic resistance and interfere the Aether

Etheral wind in experience of millimetric radiowaves propagation 213

ows. Therefore metering devices arrangement in met-al chambers is inadmissible. The reason of failures isdue 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'tbe considered as �nal experiment currently, after whichthe doubts regarding the de�nite physical concept areremoved. The matter is that within modern imagina-tion about the light speed constancy, the fact �nding ofthe Earth and Solar system motion in space availabil-ity is not enough to make a conclusion about Aetherexistence, as material medium, i.e. medium consistingof separate particles. So, Sanyak's known rotary ef-fect and the relative movement, discovered with it, forexample the Earth's diurnal rotation [23, 7], in mod-ern physics is interpreted without engaging the Aetherhypothesis existence [24]. Essentially, the attempt toshow that the discovered motion is conditioned by theEarth relative movement and Aether material medi-um were made by two explorers: Miller [5] and Staal[14], but both made the essential methodical errors.Miller placed the interferometer at di�erent altitudesand obtained that the speed of the discovered motionraised with the altitude increase over the Earth's sur-face. There shouldn't be such relation in case of move-ment in space, without Aether availability, as the mate-rial medium ow. However these major measurements,executed in [5], are methodically incorrect: the mea-surements are carried at di�erent altitudes in time; themeasurements are conducted in the environment vari-ous conditions (temperature, humidity, pressure, solarradiation, air ows, etc.), the interferometer is rathersensitive to the environment parameters variability; themeasurements, strictly speaking, are conducted by mis-cellaneous devices, since Miller's huge interferometerwas disassembled, assembled again and adjusted whilemoving from Clevelend to Mount Wilson observatory.Therefore, the technique, which Miller applied for speeddependence measurement of the discovered motion froman altitude above the Earth's surface, was unacceptableto make a �nal conclusion for the bene�t of Aetherexistence, as material medium. Staal tried to applymore correct technique for this problem solution [14].The optical interferometer mounted on an air balloon,rose up to the altitude 2500 m. The interferometer wasplaced into the pressurized metal chamber (the thermo-stat) for stabilization of the working conditions. As ithas already been emphasized, the application of metalchambers is completely inadmissible at such measure-ments. This circumstance was not known at that time.It occurred, that the measured displacement of inter-ference bands corresponds to the ethereal wind speedof 7 km/s with the error of the same magnitude order.The conclusion of the author's work [14]: \We can notdiscuss Miller's result on the basis of this experimen-tal series, as our measurements accuracy is just on theborder of Miller's observations. However we can ex-

clude Miller's e�ect, raised with the altitude increase."In other words, the motion could be �nd out, and high-altitude relation of this speed misses completely.

Thus, considering the work lacks [5, 11] and largenumber experiments availability with zero result, it ispossible to understand the physicists disbelieving to theworks at that time [5, 11], the results of which indicat-ed the necessity of the fundamental physical conceptschange.

Positive results of the data application [5, 6], at theexperiments analysis [1-4], detected reasons of unsuc-cessful attempts to repeat Miller's experiments, showed,that it is necessary to make the experiment again in or-der of the hypothesis check of the electromagnetic wavespropagation material medium | Aether existence inthe nature. It is necessary to solve the following prob-lems for this purpose. It is necessary to take into ac-count the lacks, allowed in earlier conducted researches;to apply other measurement methods, which will en-able to show the Earth's relative movement availabilityin the uni�ed measurement act in a single experimentand that the motion is stipulated by the Earth relativemovement and the material medium ow of electromag-netic waves propagation and this medium motion hasa space parentage. The positive result of such exper-iment can be considered as the experiment hypothesiscon�rmation of Aether material medium existence inthe nature.

2. Measurement method

The Aether model has been adopted as the initial hy-pothesis and o�ered in the works [21, 22, 16] whilethe experiment accomplishment. The following e�ectsshould be observed in this case at electromagnetic wavespropagation near the Earth's surface. The anisotropye�ect, i.e. wave propagation velocity depends on theradiation direction that is stipulated by the Earth andAether relative movement, i.e. the medium of electro-magnetic waves propagation. The altitude e�ect, i.e.the wave propagation velocity depends on the altitudeabove the Earth's surface that is stipulated by Aetherviscosity, i.e. the material medium of electromagnet-ic waves propagation. The space e�ect, i.e. the wavepropagation velocity along the Earth surface changesthe value within one day, that is stipulated by the spaceorigin of ethereal wind. Thus as a result of the Earth'sdiurnal rotation the altitude (astronomical coordinate)of the Solar System motion apex will change its valuewithin sidereal dayowing as for any other aster. There-fore horizontal component of ethereal wind speed and,therefore, the rate of electromagnetic waves propaga-tion along the Earth's surface will change their valueswithin the same term. Therefore, according to the re-search problems, the measurement method should beresponsive to the indicated e�ects, 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 electrody-namics [25], according to which the radiowaves propa-gation conditions from one point of a radio link to theother are completely those, as well as backwards andthis symmetry does not depend on the interspace prop-erties, which is only supposed to be isotropic. If the ra-diowaves propagation velocity depends on the radiationdirection, such space is anisotropic and the reciprocityprinciple is not applied. The ground radio link of aline-of-sight with a counter radiowaves propagation ofa millimeter-wave is used at the method implementa-tion. In this case the main �elds formation mechanizmin the acceptance points is the interference of directwaves and waves, re ected from the Earth's surface,i.e. waves, which spread at miscellaneous altitudes fromground [26]. It enables, comparing the wave interfer-ence results to �nd out the development of anisotropicand altitude e�ects simultaneously in both points. Thespace e�ect was found out, as well as in [5, 6], by theresults averaging of systematic measurements executedto scale the sidereal time S.

Let's consider the operational principle of the mea-surement method. The experience scheme is shown inthe Fig. 1

The letters A and B indicate the transceiver pointsof the radio link. Two waves come there at each of thesepoints: a straight line distributing on a pathway ABat the altitude Zup above the Earth's surface, and thewave, re ected from the Earth's surface in the pointC . The expansion of a pathway AB is r . The medi-um trajectory height ACB is Zl . The arrows indicatedas Wrup and Wrl , demonstrate the radial componentdirection of the ethereal wind speed, i.e. the compo-nent, which is operational along the radio link. Theirlengths are proportional to ethereal wind speeds at thealtitudes Zup and Zl . The radio link represents the

radio interferometer, which due to the Earth's diurnalrotation turns into the Aether ow. The characteristicsmeasurement method of the radio tracts is applied forobservation of the wave interference [27]. The methodessence is in the following. The zonding modulationsignal I with a carrier frequency f0 and the frequen-cies lower (f1 = f0 � F ) and upper (f1 = f0 + F ) ofthe lateral components (F is a modulating frequency)emits from the transmitting point. At propagation eachi signal component I receives the phase increment 'i(the indexes i = 1; 2 correspond to the frequenciesf0;1;2). The adopted signal component with the fre-quency f0 is multiplied separately from each of later-al components in the receiving device, and the phaseshift �'i is measured between the multiplication re-sults having di�erential frequencies. The expression for�'i looks like

�' = (' 0 � '1)� ('2 � '0) � (1)

Such phases combination is invariant to the time ze-ro change and received the name \a phase invariant" inthe paper [28]. Let's �nd the value �'i at a wave in-terference in the radio link points, shown in the Fig. 1.In this case, the resultant oscillation phase with i fre-quency can be determined with the following knownexpression [29]

'i = kir + arctgR sin (ki�r + �)

1 + R cos (ki� r +�); (2)

where: ki = 2�=�i is the wave number; �i = c=fi isthe wavelength; c is the radiowave propagation veloc-ity in the �xed Aether (W = 0) , in vacuum; R is themodule of the re ection coe�cient; �is the phase of there ection coe�cient; �r is the propagation di�erencebetween 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�R sin (ki�r)

1� R cos (ki�r): (3)

Let's designate

Mi = arctg�R sin (ki�r)

1�R cos (ki�r)� (4)

Let's record (3) as 'i = ki +Mi and we shall sub-stitute 'i into (1). Allowing, that

k2;1 = k0��k; �k = k0� k1 = k2� k0; we shallreceive

�' = (M0 � M1)� (M2 � M0) : (5)

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

M1 =M0 � �k�rM 0

0 +1

2�k2�r2M 00

0�


�16�k3�r3M 000

0 + � � � ; (6)

M2 =M0 + �k�rM 0

0 +1

2�k2�r2M 00

0 +

+1

6�k3�r3M 000

0 + � � � � (7)

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

�' = � (�k�r)2M 00

0 : (8)

Let's calculate the second derivative M 00

0 , then (8)will be like

�' = � (�k�r)2R�1�R2

�sin k0�r

(1 + R2 � 2R cos k0�r)2 : (9)

The expression (9) introduces the phase invari-ant value �' in an interference case in the receptionmethod point of direct waves and the waves, re ectedfrom the Earth's surface distributing on the pathwaysAB and ACB . For problem solving of the researchresults of simultaneous values measurements �'A and�'B , in the points A and B accordingly, we shalldeduct one of the other

� = �'A ��'B� (10)

In the considered method � is the measured val-ue. According to the reciprocity principle, at the ra-diowaves 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 andk0 the value �' depends on R and �r . In the paperthe data about actual values R , i.e. having a place in aradio link, selected for measurements, are obtained ex-perimentally at this radio link characteristics analysis.The informationabout the value R change range can befound, for example, in the paper [26]. The propagationdi�erence �r is determined by the radio link geome-try, but at the radiowaves propagation in atmosphere,owing to radiowaves refraction, as well the value �r de-pends upon the gradient value gn of the high-altitudepro�le of the atmosphere interception factor n (Z) [29].At the linear (and close to it) relation n (Z) the valuegn in the atmospheric layer �Z = Zup � Zl can bedetermined as

gn = (nup � nl) =�Z; (11)

where nup; nl is the index coe�cient of air at heightsZup; Zl .

The direct wave propagation velocity is (Wup =Wl = 0) the velocity of propagation of a direct waveis equal Vup = c=nup , the wave velocity, re ected from

the Earth's surface is Vl = c=nl in the isotropic case.Then (11), taking into account, that VupVl � c2 , canbe written like

gn = (Vl � Vup) =c�Z: (12)

In the anisotropic case (Wup > Wl > 0, that cor-responds the positions of an initial hypothesis) the ra-diowave propagation velocity is V and its relation tothe altitude V (Z) depend on the radiation direction,that is stipulated by the gradient medium ow of ra-diowaves propagation, i.e. Aether (Fig. 1) available. Inthis case wave propagation velocities at altitudes Zupand Zl are

Vup =c

nup�Wrup; Vl =

c

nl�Wrl; (13)

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

gn+ =1

c�Z

�c

nl+Wrl � c

nup�Wrup

�: (14)

Let's open brackets, then

gn+ =nup � nl�Znlnup

� Wrup �Wrl

c�Z: (15)

Allowing, that nlnup � 1, (nup � nl) =�Z = gn ,and (Wrup �Wrl) =�Z = gWr is the gradient of theethereal 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 high-altitude pro�le gradient of the atmosphere refractioncoe�cient gn in the layer �Z . The second memberrepresents the additional component to gn , stipulatedby the velocity gradient availability in the ethereal wind ow gWr . At the radiowaves propagation towards theethereal wind motion, it is possible to receive

gn� � gn + gWr=c� (17)

It follows from (16), (17) that if the Aether gra-dient ow is available, the wave refraction distribut-ing in counter directions, will be di�erent by virtue ofgn+ 6= gn� .

Let's consider the o�ered measurement method ac-tion with reference to a concrete experimental radiolink,taking into account the features of hardware implemen-tation of thismethod now. Let's estimate the values of probablehardware and methodical measurement errors.

216 Yu.M. Galaev

Figure 2: The experimental radiolink pro�le

3. Experimental radiolink

The measurements are conducted with the ground ra-diolink of direct visibility within 13 km. The radiolinkpro�le is shown in the Fig. 2.

The points A and B are the �nal transceiver pointsin the �gure. The point A was on the northern sideof Kharkov, the point B was in the village RussianTishky. The aerial of the point A was at the altitude 30m from the Earth's surface, and the aerial of the pointB was at the altitude 12 m. The hill top D , the terrainin the region of the point C and point B have the grasscovering. The hill top E is occupied with forests. Themedium trajectory height is AB overland Zup � 42 m.The lumen value above the top D , de�nited by geodesicmethod, is H1 � 25:3 m. The interval from the pointA up to the top Dr1 � 2200m. The azimuth of a radiolink, measured in the point A regarding the meridian,� � 450 . To specify the �elds formation mechanizmin radiolink points, the vertical �eld structure is mea-sured in the point A. The measurements are executedin summer, in August. The radiation was conducted bythe aerial of the point B on a carrier frequency of thispoint zonding signal. The vertical probing is execut-ed by consequent rise of the auxiliary receiving devicesupplied with the aerial of rather broad directional di-agram (� 100 ). The rise started from a aerial arrange-ment level of the point A . The measurement results areshown 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 indecibels regarding the reference level P0 is plotted onan abscissa axis. The height of the auxiliary receivingdevice in meters is plotted on an ordinate axis.

As it is visible from the Fig. 3, the structure of ahigh-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. Themeasured structure can be described by three wavesinterference: the direct wave (distributing on the pathes

Figure 3: The high-altitude �eld pro�le

BA), the waves, re ected from the top D (on the pathBDA), and the waves, re ected from the terrain inneighborhood of the point C (on the path BCA).

The problem solution of a �eld calculation at sever-al waves interference is described in the work [29]. Thefactor attenuation module is determined by the follow-ing formula at vertical probing

jQ (Za)j =

8><>:241 +

JXj=1

Rj cos j (Za)

352

+

+

24 JXj=1

Rj sin j (Za)

3529>=>;1=2

; (18)

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

j (Za) = 2��1�rj (Za) + �j � (19)

The propagation waves di�erence at gn = 0 is

�r0j (Za) =[Hj +�Hj (Za)]

2

2rqj (1� qj); (20)

where Hj is the lumen value above j re ection point atgn = 0; �Hj (Za) is the additional element to the valueHj , which depends upon Za ; qj = rj=r is the relativecoordinate of j of the re ection point; rj is the intervalfrom the point A up to j re ection point. The lumenvalue 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)


The calculation result is given on the right piece ofthe 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 = 25:3m; R1 = 0:07; r2 = 11000 m; H2 = 24 m; R2 = 0:04;value gn = �5:5 � 10�8 m�1 . The values R1 and R2

are obtained from the data of the �eld vertical prob-ing (left-hand piece of the Fig. 3). Their rather smallvalues (for example, in comparison with the work data[26]) are stipulated by the following features of re ectedwaves formation in an experimental radiolink (Fig. 2).It is: the waves divergence at re ection from the domedtop D ; the segment C was irradiated with a side lobeof the antenna point B direction. It is visible from theFig. 3, that the calculation results will be agreeed withthe measurement results as a whole. The di�erencesavailable can be explained by those that the calculationis executed in the supposition about the independencegn from Za .

At measurements realization, foreseen by this workproblems, the probing signals transmission in the pointsA and B was implemented by the aerials with direc-tional diagrams width � 0:50 . In this case the top Dwas outside of the aerial chart main lobe of the pointA . Therefore the signal values, received in both pointsfrom the top D directions, were much less (on 17...20dB) signal values, received from the point C directions.(As it was marked, the auxiliary aerial with the direc-tional diagram width about 100 was applied at verticalprobing and the top D was in a main lobe of such aeri-al). Therefore further estimations were executed withinthe following supposition. The signals received in thepoints A and B , represent the wave interference re-sults, which come to these points on the pathways ABand ACB . The following parameters of a re ectingsegment 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 shallreceive

�r =H2

2rq (1� q) �rH

4gn +

r3g2n32

q (1� q) : (23)

The �rst member (23), according to (20), representsthe value �r0 at gn = 0, Za = 0. The second andthird members depend on gn . Thus within the changerange gn , peculiar for atmosphere [30-32], the value ofthe third member does not exceed 0.01 from the sec-ond value. The values �r0 and rH=4 are determinedonly in geometrical parameters of a radiolink. In thiscase, neglecting third member in the expression (23)and having designated rH=4 = d , we shall receive

�r � �r0 � dgn� (24)

It follows, that anisotropic e�ects and altitudesresult 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�nedby (16), (17) in (24). Let's receive, that the propaga-tion di�erence at propagation directions concurrence ofradiowaves and ethereal wind is

�r+ = �r0 � d (gn � gWr=c) : (25)

It is at a radiowaves propagation towards the ethe-real wind motion

�r� = �r0 � d (gn + gWr=c) : (26)

It follows, that �r+ > �r , �r� < �r and �r+ 6=�r� from (25), (26). The di�erence in these valuesis determined by the velocity gradient of the etherealwind 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 receivesthe maximum value. It should be observed at the mo-ment of the ethereal wind lower transit apex (the apexcrosses the meridian in the bottom point). In [5], thedeclination 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-itude 'M = 340 n.l., the altitude above the sea levelZM � 1830 m. In [5] the ethereal wind speed in theinterferometer plane, i.e. horizontal component of thisspeed WM , was measured, it is

WM = W cos hM ; (27)

where W is the value of the ethereal wind speed moduleat the altitude ZM ; hM is the apex height in a hor-izontal system of astronomical coordinates at the lat-itude 'M . Resulting in the measured data, obtainedby Miller on Mount Wilson and in Clevelend, the high-altitude relation of the ethereal wind speed, presup-posing the exponential nature of this relation, can beapproximated 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 altitudeabove the sea level. The expression (28) enables by theresults [5, 6], obtained at the altitude ZM , to calcu-late high-altitude speed relation of the ethereal windWM (Z) at the latitude 'M . The measurements wereconducted near Kharkov, at the latitude 'K = 500 n.l.The index \K ," as well as above, means the measure-ment place. Supposing, that the nature of high-altitudespeed relation of the ethereal wind in this point of a

218 Yu.M. Galaev

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

WK (Z) = bWK (ZM )�1� e�� Z

�; (29)

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

WK (ZM ) = W coshK ; (30)

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

WK (ZM ) = WM cos hK= cos hM : (31)

Let's write down hK and hM through the apex dec-lination value �M and the latitude 'K , 'M . Let's takethe ratio for transition from the �rst equatorial systemof astronomical coordinates to horizontal ones, [33]

cos h cosA = � cos' sin � + sin' cos � cos t: (32)

Here A is the apex azimuth in a horizontal system ofastronomical coordinates; t and � is an hour angle, andthe apex declination in equatorial coordinate systemaccordingly; ' is geographic latitude of the observationplace. In a point of the lower apex transit, as well asfor any aster, A = 1800 , t = 12h (in a degree measuret = 1800 ) [33]. In this case (32) becomes

cos h = sin (� + ') : (33)

Let's substitute the values cosh , de�ned by the ex-pression (33), in (31). Allowing the latitudes values are'K , 'M and the value de�ned in [5] the apex declina-tion �M , we shall receive

WK (ZM ) = WM sin (�M + 'K) = sin (�M + 'M ) :(34)

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

WK (Z) = bWMsin (�M + 'K)

sin (�M + 'M )

�1� e��Z

�: (35)

The expression (35) allows to calculate high-altituderelation of the ethereal wind speed horizontal compo-nent for the latitude 'K by the work results [5, 6], ob-tained at the altitude zM . As the radio link is declinedfrom a meridian with the angle a, the high-altitude re-lation of the ethereal wind speed radial component inthe radio link location, at the moment of a lower apexculmination is

WrK (Z) = bWM cos�sin (�M + 'K)

sin (�M + 'M )

�1� e��Z

�:(36)

We shall �nd the high-altitude gradient relation ofthis speed, di�erentiating (36) on a variable Z . We'llobtain

gWrK (Z) = b�WM cos�sin (�M + 'K)

sin (�M + 'M )e��Z : (37)

Let's calculate the anticipated value gWrK . Thevalue WMmax � 9000 m/sec represents the averagevalue of the ethereal wind maximumspeeds in the work[5], measured during all months of observations. Havingput in (37) WM = WMmax and Z = ZK = 150 m (ZKis the radiolink altitude over the sea level), we shallreceive gWrK = 6:4 m/sec �m.

4. Instrumentation

The measurement method essence, adopted in thiswork, is described above. Let's notice the following.The expression (1) introduces a processing algorithmof the received signal I . It was shown in the work[27], that at such processing of the sources instabil-ity of the carrier and modulating frequencies do notenter in (1) and do not in uence on the value �'measurement accuracy. It has enabled to facilitatethe creation and exploitation problem of the devices,intended for phase characteristics of radiolinks mea-surement, essentially. The self-excited generators withparametric stabilization of their frequencies are appliedat the way implementation as emission sources. Theway realised in radiowaves lengths range 8mm and ear-lier was probed in [1{4]. The �nal radiolink pointswere equipped with identical complete transceiver setsas well as the recording equipment. The transmissionand sounding signals reception in each of the pointswere conducted with the same aerial. The aerials ofboth points are identical and have mirrors of diame-ters 1,1m. The generators of carrier frequencies hadthe values frequencies about 37 GHz, and generators ofmodulating oscillations 0.5 GHz. The generators fre-quencies of carrier oscillations di�ered from each otherin 50 MHz for radiated and received signals separation.The carrier frequency is f0A = 36:95 GHz in the pointA , and the carrier frequency is f0B = 37 GHz in thepoint B . The resulting power of each transmission de-vices executed on Gunn's diodes, is about 70 mW. Thegenerators of carrier and modulating oscillations withconcomitant clusters are located in thermostats. Thehardware complex contained the systems of the fre-quencies automatic tuning. The hardware has passedthe comprehensive lab tests on a board and into themeasuring complex structure within the environmenttemperatures -250C ... +350C in di�erent meteoro-logical conditions. One-channel recorders were usedfor registration in both �nal points. The additionalrecorder was used in the point A and for amplituderegistration of a received signal. This information al-lowed to distinguish the time periods, during whichthe hydrometeors (rain, snow) settled out, that wasnot always possible to determine visually. As well theamplitude channel executed the function of the workcontinuous control of the measuring system. The anal-ysis of the hardware actual characteristics and its test


results have shown, that sa is the hardware resultingroot-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 di�erence of phaseinvariants values of radiolink probing signals, receivedsimultaneously in radiolink points. Allowing (9), (25),(26), we shall write the expression for � as follows

� = ��k2�r2+R�1�R2

�sin k0B�r+

(1 +R2 � 2R cos k0B�r+)2+

+�k2�r2�

R�1�R2

�sink0A�r�

(1 + R2 � 2R cos k0A�r�)2 ; (38)

where the indexes at k0A and k0B re ect the di�erenceof probing signals carrier frequencies, received in thepoints A and B accordingly. The �rst member of theright part (38) represents the value �'A , the secondrepresents the value �'B . The expression (38) is writ-ten to conformity with the initial hypothesis position ofthe 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 getthe positive values. Let's consider the work features ofthe measurement method, which are stipulated by itsspeci�c technical implementation.

We shall consider the isotropic case (Wup = Wl =0), that corresponds to radiowaves propagation inAether, �xed regarding the observer (radiolink) at thepresence of isotropic atmosphere within the adoptedhypothesis. (It is adequate to such medium as Aetherabsence 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'ssurface V (Z) = c=n(Z). As Wup = Wl = 0 andgWr = 0, according to (25), (26), (24), we shall receive�r+ = �r� = �r . Then, if in (38) to suppose, thatk0B = k0A , we shall receive � = 0 and this equalling,according to a reciprocity principle, does not dependon the interspace properties. However, the engineeringsolution was accepted at this method implementation,in which the carrier frequencies value of probing sig-nals, emitted by each of radiolink points, di�ered. Ask0B = k0A , � 6= 0, that we shall consider �� as themeasurements error. We shall identify the values ��depending on the parameters change such as gn and Rwith (38), (24). We shall estimate probable ranges ofthe values change gn and R for the calculations ful�l-ment. The average values gn change from -4.25 �10�8m�1 in winter up to -5.95 �10�8 m�1 in summer in theair layer 25{50 m above the Earth's surface according

to the work data [30{32]. Such data take intermediatevalues in spring and autumn. The values gn change onthe average during the day as follows (-3,6 ... -4,9) �10�8m�1 in winter and (-5,5 ... -6,4) �10�8 m�1 in summer.

According to the work [26], on at tracts with grasscovering, the values change of the re ection coe�cientmodule R is within the limits of 0.2 ... 0.5 on the wave8 mm, in the season of active vegetation, up to 0.4 ...0.7 after grass withering, remaining approximately thesame if there is a friable snow cover. Thus the highestvalues of the re ection coe�cient, reached 0.7 ... 0.8,were noticed in the season of snow melting.

In the work, at �� errors calculating, the range ofthe value R change is taken within 0.03 ... 0.07, thatis stipulated by the mentioned above features of there ected wave formation in a radiolink. The selectedchange range R is matched to its change range as tothe value, measured in the work [26], and includes thevalue R = 0:; 04, which is determined in the work fromthe �eld vertical probing results in an experimental ra-diolink (left-hand piece of the Fig. 3). Such probing wasexecuted at the end of summer, when the grass cover-ing represented the withering green. It is possible tosuppose 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 partof the year, since September till January, in which themeasurements were executed. We shall use such changerange R at ful�lment of the ethereal wind parametersestimations.

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 valuesgn and the values, conforming to them Deltar , are giv-en for visualization on it. The conformity between thesevalues 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) isthe broken line. As it is visible, the curves are shiftedregarding each other. It was stipulated by the valuesdi�erence of probing signals carrier frequencies, as theresults 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 opticalinterferometer). The radio interferometer working sec-tion, within which the measurements were conducted,is indicated by the heavy straight line section in thebottom part of the piece. The same relations for val-ues R = 0:03 and R = 0:07 are re ected in the pieceby the curves �'A(gn), shown only within the radiointerferometer working section. The errors �� calcu-lation results, executed for three values R are given onthe upper piece of the Fig. 4. The value gn changerange is indicated by the broken line, i.e. the stroke

220 Yu.M. Galaev

Figure 4: The measurement error relation to the verti-cal pro�le gradient of the refraction coe�cient

section in this piece bottom, which was determinedfrom the works [30{32]. It follows from the Fig. 4 andcalculations results, that the value �� changes in allthe indicated gradient gn change range in the follow-ing limits: at R = 0:04 from ��min = 0:870 up to��max = 1:180; at R = 0:05 from ��min = 1:090 upto ��max = 1:430. The calculations have shown, thatthe error �� is systematic and can be considered asthe 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 theradiolink �nal points are arranged on concrete build-ings, the foundations of which are in an ice-free soillayer at almost constant temperature. Nevertheless,the errors calculation DFT was executed in the suppo-sition, that the whole radiolink was located on concretefoundation with the length 13000 m. It has appeared,that the value �T � 0:010 in the temperature rangegalaev:tex�T = 500C. A bit larger errors can occur ataltitudes temperature change of radiolink �nal points.��T � 0:050 at �T = 500C in this case. The cal-culations are conducted at R = 0:07. As it is visible

Figure 5: The measured value relation to the ethereal windvelocity gradient

the errors ��T are small, and they can be neglected.The executed analysis has shown, that the measure-ment method is tolerant practically in an isotropic caseto change the environment parameters. The detectederrors �� are insigni�cant and represent systematicdisplacement, which we shall consider as the correction.

In an anisotropic case (Wup > Wl > 0, that corre-sponds 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 of the relations �(gWr), executed at gn =�5 �10�8 m�1 are given for 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 de-termine the values gWr by the value � measurementresults. As the value gWr is determined as a pro�lederivative Wr(Z), so the value � is proportional tothe ethereal wind Wr speed.

The expressions (38), (25), (26) demonstrate the rel-evant property of the accepted measurement method,necessary for this research problem solving. The mea-sured value is not equal to zero (the correction value istaken into account) only in the case, when two e�ectsof the ethereal wind, i.e. the anisotropy e�ect and the


altitude e�ect, take place simultaneously. Really, it iseasy to see, that � 6= 0 only when Wrup 6= Wrl 6= 0.In other cases, when Wrup = Wrl (i.e. gWr = 0) orWrup = Wrl = 0, the measured value � = 0. In otherwords, the method is responsive to the Earth's rela-tive movement and electromagnetic waves propagationmedium| the Aether only in the case, if this mediumwill form a gradiant layer near the Earth's surface at themotion, i.e. if the medium shows the viscosity property| the property intrinsic to material mediums, whichare derivated from separate fragments. Therefore, theanisotropic e�ects and altitudes can be found out withthe reviewed measurement method in the uni�ed mea-surement act. The space e�ect also can be found in thisuni�ed measurement act, as the same measurements re-sults should be subjected to the averaging procedure inthe sidereal time scale for periodic components detec-tion.

6. The measurement technique

The probing signals IA and IB were emitted towardsone another from the points A and B accordingly. Si-multaneously the probing signals reception and theirprocessing according to the adopted measurement waywere performed in each of the points. The measuredvalues �'A and �'B were recorded on the recorders'tapes in both points. The time marks were performedin the point A and were transmitted with the signalIA to the point B . These marks were recorded syn-chronically with both points of the recorders in sucha way. The measurements were conducted continuous-ly and around-the-clock. The instrumentation calibra-tion and control of its operation implemented with theself-contained device, which performed the testing sig-nal with controled parameters and the spectrum similarto the probing signal spectrum. Such operations wereconducted at regular intervals, as a rule, 1 time for 1operating hour.

7. The processing technique ofmeasurement results

The measurement results processing of the values �'Aand �'B included the calculation procedures of themeasured value �; its diurnal variation within separatesidereal day �d(S); its diurnal variation within sidere-al day, averaged for the whole measurements cycle of� (S) ; root-mean-square deviations �� .

The values �'A and �'B were shown on sepa-rate chart tapes like continuous records. The signalamplitude record was used for the sites allocation, exe-cuted at hydrometeors falling. Such sites were removedfrom further processing. The sidereal time marks weresynchro recorded on all tapes. The values �'A(S)

Table 1: Distribution of measurement time on monthsof the year

Month of the year IX X XI XII ICommonmeasurement 278 193 165 300 352time (hours)

and �'B(S) readouts were made, they were recordedin the table of the conforming observations date fromthese tapes with the separate slide scale, in one hour ofthe sidereal time. In the same table, the values of themeasured value �(S) were recorded, calculated on theformula (10) for each of this sidereal day hours. Thesequence of such numbers obtained for separate siderealday, describes diurnal variation �d(S). The calculatedvalues were recorded in the other table. The averagevalue of the measured one was calculated for each hourof this table sidereal day

� (S) =1

�

�Xj=1

�j (S); (39)

where � is the quantity of the value � readouts, madeduring the whole cycle of measurements, in the sidere-al time equal to S . The root-mean-square deviationsof values � from its average value were calculated foreach hour of the sidereal time with the following knownexpression [34]:

�� (S) =

8<:

1

�

�Xj=1

h�j (S) � � (S)

i29=;1=2

: (40)

8. Measurement results

The results are considered in the work, which were ob-tained during 5 months, since September 1998 till Jan-uary 1999. The measurements were conducted around-the-clock, except both weekends and holidays as wellas the cases, when the electric power was not suppliedto one of the measuring points for technical reasons.The general time of continuous measurements was 1288hours. The measurement time distribution on monthsof the year is shown in the Tab. 1.

The distribution of readouts quantity of the mea-sured value �� on sidereal day time, for the wholemeasurement cycle (5 months), is shown in the Tab. 2.

In the Fig. 6 the examples of measurement resultrecords, 9 th November 1998 are shown.

The �gure is composed from pieces mated in timeof three chart tapes with the following values records:signal amplitudes, adopted in the point A (the uppercurve); 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 timeSidereal time (hour) 1 2 3 4 5 6 7 8 9 10 11 12Quantity 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 2451 52 54 55 57 54 54 57 55 55 55 58

�'B (lower curve). The pieces illustrate the typicalchanges of the registered values. Speeds of the charttapes drive are 20 mm/hour. The vertical strokes repre-sent time marks in the �gure. The digits under strokesindicate the sidereal time value in hours. The time owdirection is from right to left. The scale sections fora signal amplitude change estimation in decibels andphase invariant values change in degrees are marked inthe �gure right section. The change of time di�erencebetween the values �'A and �'B , i.e. the change ofthe measured value � = �'A��'B can be seen in the�gure. From the moment S = 14 hour up to S = 21hour, the value � has changed to � 110 . The di�er-ence between values �'A and �'B uctuations can beexplained by the following. The radiowaves are propa-gated in counter directions in a radio link. According tothe initial hypothesis, their propagation medium is theAether | material medium, having the properties ofviscous and compressible gas. The gradiant speed layeris formed in the Aether ow at Aether motion near therough surface, as well as at motion of any viscous and

compressible gas, and such motion can be accompaniedby this ow parameters uctuations. (Other causes ofsuch uctuations are possible also).

The ethereal wind speed uctuations and this speedgradient gW result in values uctuations �'A and�'B . It follows from (25), (26) and lower pieces ofthe Fig. 4, that such uctuations are counter corre-lated. The radiowaves propagation in the Aether oc-curs in isotropic atmosphere available at the same time.Known atmosphere parameters uctuations [29] alsowill result in uctuations �'A and �'B . It followsfrom (23) and lower piece of the Fig. 4, that the uctu-ations gn result in the correlated uctuations of values�'A and �'B . Therefore, the uctuations of eachvalues �'A and �'B within the adopted uctuationhypothesis are the uctuation superposition, stipulatedby 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 Aetherin counter directions, is various. The radiowaves path-ways pass with the distinguished characteristics in the


Figure 7: Mean diurnal variation of the measured value

space �eld, and the re ecting sites on the Earth's sur-face are shifted regarding each other. It can result in thevalues �'A and �'B uctuation decorrelations. Thereviewed features of the values �'A and �'B uc-tuations formation illustrate the distinctions available,which are visible in the Fig. 6.

The systematic measurement results were subjectedto statistical processing. The mean diurnal variation ofthe measured value within sidereal day � (S) is givenin the Fig. 7

The sidereal time S in hours is marked on an abscis-sa axis, the measured value in grades is marked on anordinate axis. The vertical strokes indicate con�denceintervals, de�ned as � (S) � �� (S) . It follows from aFig. 7, that the measurement results are not de�nitelyzero and are not accidental observation errors. The re-lation � (S) has the expressed form of the varied valuewith the period, equal to one sidereal day, i.e. the mea-sured e�ect has a space parentage. It is shown above,that the measured value is not equal to zero point onlyin the case when two e�ects of the ethereal wind, i.e.an anisotropies e�ect, stipulated by the Earth's relativemovement and radiowaves propagation medium as wellas the altitude e�ect, stipulated by the speed gradiantlayer in this medium ow available, take place simulta-neously. The positive measurement results, given in theFig. 7, demonstrate, that these both required etherealwind e�ects take place simultaneously. Therefore, thespace e�ect development, the anisotropy e�ect and the

altitude e�ect are shown in the uni�ed experiment, inthe uni�ed measurement act.

Let's compare the measurement results of the workto the results [5] and [11]. We shall use maximum rat-ings of the measured values at matching. We'll de�nethe values gWrK with the relations �(gWr), which weregiven in the Fig. 5. We shall call such values gWrK

to be measured. The measured gradient values of theethereal wind speed horizontal component gWK can befound as follows

gWK = gWrK= cos�; (41)

that follows from the expressions (35) - (37) results.The expression (37) allows to compare the measurementresults of the work to the data [5, 11]. Really, havingput 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 valuesWM with the measured values gWrK . We shall des-ignate the values WM, calculated with (42), as WMK

and treat this value as follows: WMK is the horizontalcomponent of ethereal wind speed on the geographiclatitude 'M , the altitude ZM , calculated by the mea-surements results of the ethereal wind velocity gradientat 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 theethereal wind speed in a radiolink can be determinedwith the following expression

WrK = gWrK

�e�ZK � 1

�=�: (43)

This speed horizontal component is equal accord-ingly 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 etherealwind and the work results [5, 11] are listed in Tab. 3.

The �rst column of the Tab. 3 represents the valuemeasurements result � (S)max in grades. The columns2,3,4 are the calculation results of the ethereal windparameters executed with the expressions (41), (44),(42) accordingly. The data about the ethereal windparameters are shown in the table like fractions. Mul-tipair numerator corresponds to the parameter valueobtained at R = 0:04, and denominator - at R = 0:05.Such form of the measurement results representation isstipulated by those, that the systematic values R mea-surement was not conducted during the experiments.The digit in the column 2, given in brackets, representsthe calculated value gWK with (37), (41), that we shall

224 Yu.M. Galaev

Table 3: The ethereal wind parameters1 2 3 4 5 6

�, grade gWK ;m=s�m WK , m/s WMK , m/s WM , m/s [5] WM , m/s [11]14 8;63

6;22 ; (9,05)14141019

84906124 9000 6000

call as the anticipated ethereal wind velocity gradientvalue in Kharkov. The column 5 represents the max-imal ethereal wind speed value, obtained by Miller atmeasurement results averaging, executed in the obser-vatory Mount Wilson in April, August and September1925 [5]. The column 6 represents the maximal etherealwind speed value, measured in the observatory MountWilson in the experiment [11], 1929.

The executed estimations have shown, that the hor-izontal component of ethereal wind speed reaches thevalue WK � 1414 m/s in Kharkov. This work measure-ment results are recalculated to the observatory MountWilson location with the expression (42). The obtainedvalue WMK � 8490 m/s, that is close to the result [5]WM = 9000 m/s. A bit smaller values WMK (allowingthe estimations at R = 0:05), in comparison with theresult [5], can be explained with di�erent conditions ofthe experience realization. The cross-country terrainsmeasurement are conducted on the slightly cross ter-rain. The ambient relief altitudes di�erence is about 20m. The experiment [5] was executed at a mountain topand the ambient terrain was much below the measure-ment conducting place. It can be supposed, that in the�rst case the terrain ambient relief a�ect on the etherealwind speed value is more, than in the case of the work[5]. Such supposition about the surface and local sub-jects in uence (hills, buildings, located closely to theradiolink, etc.) has been con�rmed at the results com-parison [5] and [11]. So, the ethereal wind speed smallervalues in [11] in comparison with the data [5] are ex-plained in [7] by Aether ow deceleration with buildingswalls, in which there was this work author's interfer-ometer [11]. Miller [5] built a light wooden house forthe measurements realization in the observatory MountWilson. There were continuous windows made of whitecanvas on all its sides. In 1929Michelson, Peas, Pearson[11] conducted the similar experiment in a fundamentalbuilding of an optical workshop in Mount Wilson ob-servatory. The ethereal wind measured speed was nomore than 6000 m/s as a result.

The ethereal wind speed value, measured in a radiofrequency band at the work, is close to the ethereal windspeeds values, measured in electromagnetic waves opti-cal range in the experiments of Miller [5, 6], Michelson,Peas, Pearson [11]. Such comparison results can be con-sidered as mutual con�rmation of the research resultsveracity, the experiment [5, 6] and the experiment [11].

The ethereal wind velocity gradient measurements

were not performed in former works, we can comparethe measured values gWK with the anticipated (calcu-lated) value. As we can see from the table 3 (column2) the value gWK measurement results are close to itscalculated value.

The executed analysis has shown, that this work re-sults can be explained by radiowaves propagation phe-nomenon in a space parentage driving medium witha gradiant layer speed in this medium ow near theEarth's surface. The gradiant layer available testi�esthat this medium has the viscosity | the property in-trinsic material media, i.e. media consisting of separateparticles. Thus, the executed experiment results agreewith the initial hypothesis positions about the Aethermaterial medium existence in the nature.

9. Conclusion

The parameters measurement method of anisotropicmedia of electromagnetic waves propagation was o�eredand realised in the range of millimeter radiowaves at thework. The systematic experimental research results, ex-ecuted near the Earth's radiolink of a line-of-sight, haveshown:

| the Earth's relative movement and radiowavespropagation medium available;

| the radiowaves propagation medium ow has aspace origin;

| the radiowaves propagation medium has the vis-cosity | the property intrinsic to material media con-sisting of separate particles.

The work results can be considered as the experi-mental hypothesis con�rmation about the existence ofsuch 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 circuitof millimeter radiowave range." Scienti�c instrumentmanufacture in mm. and sub. mm. radiowaves frequen-cy bands: Digest of scienti�c works Kharkov: Instituteof radiophysics and electronics engineering of NSA inUkraine. 1992, pp. 63{72.

[2] F.V. Kivva, Yu.M. Galaev, \Dispersion e�ects in fre-quency windows of mm wave range radio waves." At-mospheric Propagation Technical Exchange Proceed-ings: ARL, Orlando, FL, USA. 1993, pp. 509{517.


[3] Yu.M. Galaev, \Model of radiowave dispersion in atmo-sphere." Atmospheric Propagation and Remote Sens-ing 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 communica-tion line of millimeter radiowaves band . Experiment.Model." 7-th International Crimean conference \Mi-crowave technique and telecommunication technolo-gies" (CrMiCo 97). The conference papers: Sevastopol,Crimea, Ukraine. 2, 1997, pp. 670{673.

[5] D.C. Miller, \Signi�cance of the ether-drift experi-ments of 1925 at Mount Wilson." Science, LXIII, No.1635, pp. 433{443 (1926).

[6] D.C. Miller, \The ether-drift experiment and the de-termination of the absolute motion of the Earth." Rev.Modern. Phys., 3, 203{242 (1933).

[7] \Ethereal wind." Digest by Dr. in Sc. V.A. Atsukovsky.Moskow, Energoatomizdat, 1993, 289 pp.

[8] A.A. Michelson, \The relative motion of the Earth andthe Luminiferous ether." The American Journal of Sci-ence, III series, XXII, 128, 120{129 (1881).

[9] D.C. Miller, \Ether-drift experiment at Mount Wil-son." Proc. Nat. Acad. Amer., 11, 306{314 (1925).

[10] S.I. Vavilov, \New \ethereal wind" searches." Successesof physical sciences, 6, 242{254 (1926).

[11] A.A. Michelson, F.G. Pease, F. Pearson, \Repetitionof the Michelson - Morley experiment." Journal of theOptical 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 - Morleyexperiment." Proc. Nat. Acad. Sci. of USA, 12, 621{629 1926.

[13] K.K. Illingworth, \A repetition of the Michelson-Morley experiment using Kennedy's re�nement." Phys-ical Review, 30, 692{696 (1926).

[14] E. Stahel, \Das Michelson - Experiment, ausgefurt imFreiballon." Die Naturwissenschaften, Heft 41, 8, 10,935{936 (1926).

[15] G. Joos, \Die Jenaer Widerholung des Mihelsonver-suchs." Ann. Phys., 7, 385{407 (1930).

[16] V.A. Atsukovsky, \General etherdynamics. Simulationof the material and �eld structures on the basis of theimaginations about the gas like Aether." Moscow, En-ergoatomizdat, 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 rel-ativity." Phys. Rev. Letters, 1, 9, 342{349 (1958).

[19] D.C. Cyampney, G.P. Isaac, M. Khan, \An ether driftexperiment based on the Mssbauer e�ect." Phys., Let-ters, 7, 241{243 (1963).

[20] T.S. Jaseja, A. Javan, J. Murray, C.H. Townes, \Testof special relativity or of the isotropy of space by use ofinfrared masers." Phys. Rev., 133a, 1221{1225 (1964).

[21] W. Azjukowski, \Dynamik des Athers." Ideen des ex-akten Wissens, Stuttgart, 2, 48{58 (1974).

[22] V.A. Atsukovsky, \The introduction into etherdynam-ics. Model imaginations of material and �eld struc-tures on the basis of gas like Aether." Moskow, MOIP,physics dep., 1980. | Dep. in VINITI 12.06.80 No.2760-80 DEP.

[23] A.A. Michelson, H.G. Gale, Assisted by F. Pearson.\The e�ect of the earth's rotation on the velocity oflight." Part II. The Astrophysical Journal, LXI, 5, 140{145 (1925).

[24] S.N. Stolyarov, \Sanyaka's experience." The Physicalencyclopaedic dictionary. Moskow, The Soviet encyclo-pedia, 1965, 4, 466 pp.

[25] V.V. Nikolsky, T.I. Nikolskaya, \Electrodynamics andradiowaves propagation." Moskow, Nauka, 1989, 544pp.

[26] G.P. Kulemin, V.B. Razskazovsky, \Dissipation of mil-limeter radiowaves by the Earth's surface at small an-gles." Kiev, Nauk. dumka, 1987, 232 pp.

[27] A.s. 1337829 USSR, MKI4 G01R29/00. \The mea-surement way of radiotracts characteristics." /Y.M. Galaev, B.V. Zhukov, Bul. ed., 34, 183 (1987).

[28] V.A. Zverev, A modulation measurement method ofultrasonic dispersion." The Reports of NSA USSR, 91,4, 791{794 (1953).

[29] A.I. Kalinin, E.L. Cherenkova, \Radiowaves propaga-tion and radiolinks operation." Moskow, Svyaz, 1971,440 pp.

[30] E.E. Vyaltseva, \Variability of the atmosphere refrac-tion factor for a MWF in a boundary layer," Meteorol-ogy and hydrogeology, 2, 8{14 (1972).

[31] E.E. Vyaltseva, \Variability of the air refraction indexfor a MWF in a 300-m layer in winter." Ed. IEM, 1974.Iss. 6 (44), pp. 99{105.

[32] G.N. Lipatov, O.Ya. Aksakova, \Some features of di-urnal pass and vertical pro�le of radiowaves refractionindex in lower 500m atmospheric layer." Ed. TSVG-MO, 1977, iss. 9, pp. 71{78.

[33] V.K. Abalakin, E.P. Aksenov, E.A. Grebennikov, etc.\Guide on a celestial mechanics and astronomy dynam-ics." Moskow, Nauka, 1976, 864 pp.

[34] L.Z. Rumshisky, \Mathematical processing of the ex-periment results." Moskow, Nauka, 1971, 192 pp.


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 uidapproximation and with the mass density distribution �(x) = �0(1� x2� )

n

are solved ( �0 is a center density,x = r=R; R is the radius of star). By means a method of successive approximations with a small compactnessparameter � = 2M=R (M is mass of star) the analytical solution of approximative Einstein's equations for integervalue of n parameter is received. Models of three fundamentally di�erent astrophysical objects are considered. Theseare a neutron star (n = 1, � = 1, � = 0:147), the white dwarf Sirius B (n = 5, � = 1, � = 1:3 � 10�4 ), stars ofmain 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 possiblecompactness is determined. Results of calculations with known observational data were correlated.

1. Introduction

At modelling of such astrophysical objects as stars, fre-quently it is possible to not take into account dynamicprocesses account into them running. The necessity ofthe account of changes arises then, when the star or ro-tates, or fast loses the mass at the expense of radiativesublimation of the matter [1] and radiation. In othercases the physical description of stars in the assumptionof their static character is admissible.

In the present article the descriptive attempt ofphysical star properties for di�erent types of stars with-in the framework of one approach is realized. At mod-elling except for static character of a star, it suggestsits spherical symmetry. The space-time geometry ofsuch object interior gravitational �eld we shall describeby a 4-interval

ds2 = F (r)dt2 + 2L(r)dtdr � r2(d�2 + sin2�d'); (1)

where functions F (r) and L(r) are metric coe�cients.We use here a geometrical system of units in whichvelocity of light and gravitational constant are equalto unit. The Einstein equations are solved with aenergy-momentum tensor in perfect non-viscous uidapproximation and with the mass density distributioninside a star as

�(x) = �0(1� x2�)n; (2)

1e-mail: [email protected]: [email protected]

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 = 1gEinstein equations are solved analytically. If n = 0,we have the interior Schwarzschild solution [2], and iff� = 1; n = 1g , we have an exact solution for parabolicmass density distribution [3].

2. Mathematical model

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

" = 1� �

x

Z�(x)x2 dx; (3:1)

G00 +d

dx

�ln

p"

x

�G0 +

"0x+ 2(1� ")2x2"

; (3:2)

~p0 = �~p2 x2"

+ ~p ��" � 1� ~�x2

2x"

�+

~�(" � 1)

2x"; (3:3)

where " = F=L2 ; G =pF ; ~p = �p ; ~� = �� ; � =

8�R2 ; p(x) is a pressure; a prime means derivativeon x .

The central of energy density�0 is connected witha central pressure p0 by means the Fermi degeneratedrelativistic 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 Schwarzschildgive 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 thestar mass.

Now we have system (3) with three equations andfour unknown functions. These function are �(x),p(x), "(x), G(x). For closing given system of equa-tions we shall add to it the mass density distribution(2).

Thereby, expressions (2-4) describe the mathemati-cal model of our problem. Given model has no analyt-ical solutions under integer values of parameter n > 1.

3. Integration of Einstein equations

For integer values of parameter n we may multiply outof the expression (2) by means the formula of binomialtheorem. Then equation (3.1) is integrated and we haverelation

"(x) = 1� � � �(x)=�(1) (5:1)

with

�(x) =nXj=0

Cjn(�1)j2j� + 3

x2j�+2 (5:2)

and following equality

� = ��0�(1): (6)

In the expression (5.1), constant of integration is putequal to zero for restriction of function "(x) in the starcenter. 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 isa main idea of our paper.

We de�ne function (x) for further calculations as (x) = �(x)=(x2�(1)).

Thus,"(x) = 1� � � x2 (x): (7)

On physical sense the function is the ration of av-erage mass density of the star interior part with radiusx > 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 serieson compactness:

G(x) =1Xk=0

�kGk(x): (9)

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

�G0k+1=x

�0= �Qk(x); (10:1)

G0 = 1; (10:2)

where

Qk(x) = x (x)G00k(x)+x 0(x)G0k(x)=2+

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

Expression for function F (x) may be written nowin the following form

F (x) =1Xk=0

�kFk(x) = G2(x) (11:1)

with

G2(x) =1Xk=0

0@�k �

kXj=0

GjGk�j

1A: (11:2)

Integrating twice expression (10.1), �nally is ob-tained

Fk(x) =kX

j=0

�~Qj(x) + C

(j)1 x2=2 + C

(j)2

��

��~Qk�j(x) + C

(k�j)1 x2=2 + C

(k�j)2

�; (12:1)

F0 = 1; (12:2)

where

~Qj(x) =

Zx

�ZQj(x) dx

�dx; (12:3)

C(j)1 C

(j)2 are constants of integration. These con-

stants are de�ned on each step k of iterations from thefunctions Fk(x) junction conditions on the star surfacewith external Schwarzschild �eld

F (x = 1) = 1� �) Fk(x = 1) = �0k � �1k; (13:1)

F 0(x = 1) = �) F 0k(x = 1) = �1k; (13:2)

where �jk is the Kronecker symbol.Thus, the expressions (12) are the formulas of the

function F (x) progressive approximationsmethod oversmall parameter � . That the integrand functions in(12.3) represent the sums of various real degrees x , wehave no problems with calculation of analytical expres-sion for k-approximation function Fk(x) accoding toformula (12.1).

228 Alexandre Baranov and Michael Lukonenko

Table 1: Parameters of prototyped starsType R M �0 nof star [cm] [MJ] [g=sm3]

A 1 � 106 1 1 � 1015 1B 2:02 � 109 0:89 1:3 � 1010 5C 6:96 � 1010 1 142:54 25

Table 2: Result of modellingType of stsr p0[din=sm2] Vsound(x = 0)[c]

A 5:84 � 1033 0:21B 2:38 � 1022 6:68 � 10�3C 3:46 � 106 1:64 � 10�3

We shall �nd an approximate expression for thesecond metric factor L(x), using the relation "(x) =F (x)=L2(x) and equality (7). Especially we shall markthat function

F (x) =1Xk=0

Fk(x) (14)

is the exact solution of system equations (2-4) underchoice 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) andequality (6) the relation follows

nXj=0

(�1)j2j� + 3

=2M

8��0R3: (15)

One allows to coordinate parameters n and � in theleft-hand part with physical characteristics of the star.

We obtained the following values of parameter n (at� = 1) for di�erent three types of stars. Type A is aneutron star, type B is a white dwarf (the Sirius B) andtype C is a star of main sequence (the Sun).

The values of parameter n in Tab. 1, have someinaccuracy, connected with properties of the equality(15). The left-hand part of this equality is discrete, butright part is continuous. Therefore not always there is apossibility to select for a concrete star an integer valueof parameter n , satisfying (15).

Under the formula (12) the analytical expression ofan approximate solution of the system of equations (2-4) for three types of stars was obtained (Tab. 1). Cen-tral values of pressure and sound velocities Vsound wereobtained as the result of our modelling.

Results of calculations were correlated with knownobservational data. For example, for the Sun model wehave following facts, described in [4]:

1. value p0 from Tab. 2 di�ers from known on 2% ;

Table 3: Limiting values of compactnessn 0 1 2 3 4 5

�max 0:14 0:21 0:20 0:18 0:16 0:14

Table 4: Critical parameters of starsfn; �g M�[MJ] R�[km]

f0:2; 1g 1:65 16:69f1:4; 1g 0:85 9:58f2:6; 1g 0:62 7:43f3:8; 1g 0:52 6:39f1:0; 1g 0:46 5:78f20; 1g 0:30 3:66f1; 0:2g 1:65 16:69f1; 1:4g 0:85 9:58f1; 2:6g 0:62 7:43f1; 3:8g 0:46 6:39f1; 1:0g 0:42 5:78f1; 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 solarkernel on the order is less central value.

5. Stability of model

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

1. Oppenheimer{Volko� criterion of stability [5]:dM=d�0 < 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 �xed values of parameters n and � .These restrictions are in Tab. 3. f� = 1; 0 � n � 5g .

The stability criterion

dM=dR < 0; (16)

is equivalent to Oppenheimer{Volko� criterion. Thiscriterion allows to �nd maximum of star masses M�

and minimum of star radii R� , which characterized by�xed values of parameters � and n . These restrictionsfor f� = 1; 0 � n � 5g and fn = 1; 0:2 � � � 20g arelocated in Tab. 4.

Comparing modelling data (Tabs. 1, 2) and restric-tion on use of model (Tabs. 3, 4, 5) we may concludeabout 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 themain sequence of stars.

Let's note that in paper [6] the star models withthe energy density distribution of the type (2), howeverconsideration was limited by f� = 1; n = 1; 2; 3g .

6. Conclusion

In summary, it is necessary to note that the choice ofthe mass density distribution as type (2) does not re-strict applicabilities of our method. For realization ofsuccessive approximations method it is necessary to in-tegrate the expressions (3.1) and (12.3) only.

The paper is realized in framework of the Federalprogram 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," ForeignLiterature, Moscow, 1963, p.244 (in Russian).

[3] A.M.Baranov, Dep. in VINITI 13.07.76, 2626-76 (inRussian).

[4] \Physical encyclopedic dictionary," eds. A.M. Prohorov,Soviet encyclopedia, Moscow, 1983 (in Russian).

[5] J.R. Oppenheimer, G. Volko� in: \Albert Einstein andgeneral relativity," Mir, Moskow, 1979, p.337 (in Rus-sian).

[6] H. Knutsen, Gen. Rel. and Grav., 22, 925-946 (1967).

[7] A.M. Baranov, M.V. Lukonenko, S.F. Tegai, Abstractsof Intern. Confer. \Geometrization of Physicis III",\Hater", Kazan, 1997, 6 (in Russian).


ON FIXED SINGULARITIES IN KERR-SCHILD SPACES

Alexandre Baranov1 and Sergei Tegai1


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-freenull congruence. Function F (G; �1; �2) determining implicitly the null congruence is choosen in the general formof squre polinomial. The discriminant of the polinomial describes common singularities of the electromagnetic andgravitational �elds. It is shown that all �xed singularities are intersections of two second order sufaces. For examplethe ring singularity of Kerr-Newman solution is an intersection of a sphere and a plane passing through the centerof 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�� = �� 2Hk�k�; (1)

where �� is Minkowskian metric; H is a scalar func-tion; k� is a null vector for both metrics g�� and �� :

g��k�k� = ��k

�k� = 0: (2)

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

�k�dx� = �Gd� +G�� + G �Gdv + 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; �2) is an arbitrary analytic function of threecomplex variables G; �1 = ��G+ u; �2 = vG+ �:

Common singularities of the electromagnetic andgravitational �elds are given by dF=dG = 0. Solu-tions with singularities bounded in three-space are ofthe most interest for star exterior modelling.

2. Linear case

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

F = a1�1 + a2�2 + a3G+ b1: (5)

1e-mail: [email protected]

The condition for singularity

dF=dG = a1�� + a2v + a3 = 0 (6)

is a system of two real linear equations. Both describethree-dimentional hyperplanes in four-space. So thesingularity can't be �nite in linear case.

3. Square case

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

F = b1�21 + b2�1�2 + b3�1G+ b4�

22 + b5�2G+

+b6G2 + c1�1 + c2�2 + c3G+ d1: (7)

The condition dF=dG = 0 is equivalent to the equiationD = 0; where D is a discriminant of square polinomialF (G).

Only �xed singularities are considered later. Thismeans that D must not depend on x0: As D is a fourth

degree polinomial all it's terms with x04; x0

3xi; x0

2xi2

and others containing x0 must be equal to zero. All thediscriminant's terms of fourth degree can be written inthe form (b22� 4b1b4)(x0

2�x12�x32�x42)2 . And theterms of the third degree can be written in the form

(x02 � x1

2 � 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 ordersurfaces 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 coe�cients with x02; 2x0x1;

2x0x2; 2x0x3; x0 correspondingly. These constraintslead to the following cases:

1 b2 = b1 = b4 = 0:1.1) b3 � c2 = 0:1.2) b3 � c2 = 1:

2 b2; b1; b4 are not equal to zero at the same time.2.1) b3 6= 0; b5 6= 0; b3c2 = b5c1 6= c3:2.2) c1 6= 0; c2 6= 0; b3c2 = b5c1 6= c3:2.3) 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 thesimple shape of

a21 + a22 + a23 = 0 (18)

and

a0a1 = a0a2 = a0a3 = 0: (19)

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

~D = a21x12 + a1a2x

1x2 + a1a3x1x3 +

+a22x22 + a2a3x

2x3 + a23x32: (20)

The singularity described by it is a line. The linear partof the discriminant in uence only on the location of theline and can be easily eliminated by linear substitutionof coordinates.

1.2 In this case we get the Kerr-Newman solution[2]. The discriminant has the form of

D = (x12+ x2

2+ x3

2) + c23 � 4b6d1 +

+2((b6 � d1)x1 + i(b6 + d1)x

2 + c3x3): (21)

It's real part is a sphere and it's imaginary part is aplane passing through the center of the sphere. Thereintersection is a ring singularity of the Kerr-Newmansolution.

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

The equations (9)-(12) are linear and homogeneous onvariables b2; b1; b4 . So b2; b1; b4 are not simultaneouslyequal to zero only when the rank of the system is lessthen three. This is equivalent to

4(b3c2 � b5c1) = a20 � a21 � a22 � a23 = 0: (22)

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

c23 � 4b6d1 = 0: (23)

With (8) and (22) this gives us the degenerate complexquadric 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 =b32b5

; b4 =b52b3

; c2 =b5c1b3

; (24)

2b6 = 2c3b4 + (b3 � c2)b5; (25)

2d1 = 2c3b1 � (b3 � c2)c1: (26)

Characteristic quadric form ~D of the discriminant isproportional to

~D � (b23 � b25)2x12 � 2i(b23 � b25)(b23 + b25)x

1x2 ��4b3b5(b23 � b25)x1x3 � (b23 + b25)

2x22+

+4ib3b5(b23 + b25)x

2x3 + 4b23b25x

32: (27)

Both real and imaginary parts of it have eigenvalues

[0; (b3�b3)2 + (b5�b5)

2;�(b3�b3)2 � (b5�b5)2]: (28)

2.2 Analogously with 2.1 we obtain

b1 =c12c2

; b4 =c22c1

; b5 =c2b3c1

: (29)

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

~D � (c21 � c22)2x12 � 2i(c21 � c22)(c21 + c22)x1x2 �

�4c1c2(c21 � c22)x1x3 � (c21 + c22)

2x22+

+4ic1c2(c21 + c22)x

2x3 + 4c21c22x

32 (30)

and it's eigenvalues

[0; (c1�c1)2 + (c2�c2)

2;�(c1�c1)2 � (c2�c2)2]; (31)

2.3 In this case we can assume b1 = f1d1; b2 = f1c3;b4 = f1b6; c3 = 2f22 d1; b6 = f2d1 , where f1 6= 0because all of bi are not equal to zero, and we have

~D � (1� f22 )2x1

2 � 2i(1 � f22 )(1 + f22 )x1x2 �

�4f2(1� f22 )x1x3 � (12 + f22 )2x2

2+

+4if2(1 + f22 )x2x3 + 4f22x

32: (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 linearcase. For �xed singularity b5 = 0:

232 Alexandre Baranov and Sergei Tegai

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 sin-gularity of the Kerr-Newman solution and the secondone is a line. So we can conclude that for obtaining ofnonstationary solutions by Kerr-Schild method we needto choose higher degree of F or consider the singulari-ties depending on time.

The paper is realized in framework of the Federalprogram 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).


ALGEBRAIC CLASSIFICATION OF 5D KRISHNA

RAO WAVE SOLUTION

Alexandre Baranov1 and Nikolai Bardushko2


660041, Russia

Received December 14, 2000

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

1. Introduction

In general relativity wave solutions investigation is oneof the most important problems. The same metric invarious coordinates looks di�erently. Sometimes it isdi�cult to say, whether the solution of the Einsteinequations belongs to a wave type or not. As a rule onthis problem there can not be an answer basing only onappearance of the metric. So it is necessary to use spe-cial invariant methods for detection of wave propertiesof space-time.

Petrov's algebraic classi�cation of gravitational�elds is such method in 4D space-time [1]. Here weconsider space-time as space with a time-like directionboth 4D and 5D space-times. Using a symmetry ofthe curvature tensor subscripts the Riemann tensorof 4D space-time into symmetrical traceless complex3 � 3 the Weyl matrix may be mapped. An eigen-values problem of such Weyl matrix solves the taskof algebraic classi�cation of gravitational �elds in 4Dspace-time. Depending on Weyl matrices' eigenvaluesand eigenvectors we have seven matrix canonical sub-types, i.e. in 4D space-time only seven various algebraicsubtypes of gravitational �elds exist or total three typesby Petrov [1].

It is known that gravitational �elds of various typeson Petrov have di�erent the Segre characteristics of theWeyl matrix. The analysis of wave criterions in 4Dspace-time was investigated in details in [2]. In thatclassi�cation wave solutions correspond to algebraicallyspecial types N and III as rule. The Segre characteris-tics of the Weyl matrices are [(2 1)] and [(3)] respective-ly and type N describes pure gravitational wave. Some-times type II is considered as a wave algebraic type. In

1e-mail: [email protected]: cut [email protected]

reality the type II describes mixed gravitational �eldswith wave propeties and has the Segre characteristic ofthe Weyl matrix [2 1]. The Weyl matrix canonical formof 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 ob-tained from the curvature tensor of Riemann. That iswhy it is so important to extend the 4D Petrov's alge-braic classi�cation onto 5D space-time of Kaluza. Anattempt of such extension and algebraic classi�cationof some solutions was undertaken in [3]. According tothis approach the conformal curvature tensor of Weylfrom the Kaluza space-time is mapped to symmetricaltraceless 10 � 10 Weyl matrix and the 5D space-timeis mapped to 10D manifold of bivectors. Then it issolved the matrix eigenvalue problem in general case toclassify the Kaluza space.

3. Krishna Rao generalized solution

Metric element of the 5D space-time we will take as

ds2 = e2k(dt2 � d�2) � �2d'2 � dz2 � e2mdu2; (1)

where

k = k(t � �); m = m(t � �):

This metric element generalizes Krishna Rao wavesolution [4] onto 5D Kaluza-Klein theory. Let us toclassify corresponding Weyl tensor by means of ideasfrom [3].

234 Alexandre Baranov and Nikolai Bardushko

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

�(0) = ekdt; �(1) = ekd�;�(2) = �d'; �(3) = dz;�(5) = emdt:

(2)

Nonzero conformal curvature Weyl tensor compo-nents in basis (2) are

W(0)(1)(0)(1) =W(2)(3)(2)(3) = W(3)(5)(3)(5) = _mA;W(0)(2)(0)(2) = A(�B + 4 _k � _m);W(0)(2)(1)(2) = A(B � 4 _k);W(0)(3)(0)(3) = �A(B + 2 _k � _m);W(0)(3)(3)(1) = A(B + 2 _k);W(3)(1)(3)(1) = �A(B + 2 _k + _m);W(1)(2)(1)(2) = A(B � 4 _k � _m);W(0)(5)(0)(5) = �A(B � 2 _k � _m);W(0)(5)(1)(5) = A(2B � 2 _k);W(1)(5)(1)(5) = A(2B � 2 _k + _m);W(2)(5)(2)(5) = �3 _mA;

(3)

where

A =e�2k

6�; B = 2( �m + _m2 � 2 _k _m)�:

Weyl tensor may be mapped onto 10D bivector man-ifold by following manner. Each pair of antisymmetri-cal subscripts is represented as a new subscript. Thissubscript rule of mapping is

01! 1; 02! 2; 03! 3; 23! 4;31! 5; 12! 6; 05! 7; 15! 8;

25! 9; 35! 10:(4)

The mapping reduces the Weyl tensor to symmetri-cal 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 di�erent physi-cal �elds in 4D space-time: Wf1::6; 1::6g describes thegravitation; Wf1::3; 6::10g corresponds to the electric�eld; Wf3::6; 6::10g corresponds to the magnetic �eld;Wf6::10; 6::10g corresponds to a scalar �eld.

Now we set put an eigenvalue problem for the Weylmatrix (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 rota-tions of basis (2) in 5D. By means of such elementarytransformations �{matrix may be reduced to canonicalform

W(�) =diag(1; 1; p1; p1;�p1;�p21;�p21; p2; p3; p4); (7)

where diagonal components of �{matrix (7) are theelementary divisors of eigenpolinomial (6) with theirmultiplicity and

p1 = � � �1 = �� _mA;

p2 = �� 2 = �� (�3 _mA);

p3 = �� 3 = �� (� _k � _m �q17 _k2 + 8B _k)A;

p4 = �� 4 = �� (� _k � _m +

q17 _k2 + 8B _k)A;

Segre characteristic in this case is

[(11)(122)111]: (8)

A metric with the characteristic (8) belongs to alge-braically special metric types . Our �{matrix (6) haselementary divisors with double multiplicity.

As well as in the Petrov algebraic classi�cation let uscall it as II type. In this case every elementary divisorhas its eigenvector. Eigenvectors are lightlike if they be-long to the elementary divisors with double multiplicityor more. Eigenvectors in the 10D manifold de�ne in-variant directions in 5D space-time. The lightlike bivec-tors correspond to light-like invariant directions. So thealgebraic classi�cation may be used to determine wavestructure of space-time. If a space-time is described bythe Weyl matrix (5) with elementary divisors of doublemultiplicity or more then it has wave structure.

The considered 5D space-time with the metric ele-ment (1) has the Weyl matrix's (5) elementary divisorsof double multiplicity (see (5)). These divisors corre-spond to following lightlike bivectors

e1 = �(0) ^ �(2) + �(1) ^ �(2);e2 = �(0) ^ �(5) + �(1) ^ �(5): (9)

Algebraic classifcation of 5D Krishna Rao wave solution 235

Bivectors (9) de�ne lightlike directions in 5D space-time

l1 = �(1);l2 = �(5):

(10)

Thus 5D space-time with metric (1) has wave struc-ture and the Krishna Rao generalized solution preservesits wave structure, but it is more general solution.

In 4D space-time the Krishna Rao metric belongsto the type N of Petrov's algebraic classi�cation. Forthis type of space-time the Weyl matrix has elementarydivisors with double multiplicity and eigenvalues whichare equal to zero.

To have complete correspondence in 5D space-timewith the 4D algebraic classi�cation we should require

� =_m

6�e�2k = 0: (11)

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

4. Energy-momentum tensor

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

R(�)(�) � g(�)(�)R = �kT(�)(�); (12)

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

T(�)(�) =

0BBBB@

T(0)(0)T(0)(1)T(0)(1)T(1)(1)

0T(3)(3)

0

1CCCCA ; (13)

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

T(0)(0) = (B � 2 _m+ k)=�;

T(0)(1) = �(B + _k)=�;

T(1)(1) = �(B + 2 _m+ k)=�;

T(3)(3) = 2 _me�2k=�:

It is seen that the energy-momentum tensor haswave structure, i.e. it has lightlike eigenvectors. Accor-ding to an algebraic classi�cation of symmetric secondrank tensors the tensor (13) belongs to the class II ofsuch classi�cation.

5. 4D projection

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

4g�� = g�� g5�g5�g255

; (14)

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

4ds2 = e2k(dt2 � d�2)� �2d'2 � dz2; (15)

which is the Krishna Rao 4D metric for the pure radi-ation.

6. Conclusion

The wave properties of the 5D Krishna Rao's genera-lized solution have been investigated. We used an ap-proach which is written in [3] and permits to genera-lize the 4D Petrov algebraic classi�cation on 5D Kaluzaspace-time. It was shown that new 5D metric belongsto algebraically special type (in the sense of the 5D al-gebraic classi�cation), analogous to the type II of thePetrov classi�cation. The research of physical mean-ing of the 5D energy-momentum tensor is a problem offollowing investigation. The algebraic classi�cation of5D spaces may be used to systematize space-times, toanalyze and to search new solutions.

References

[1] A.Z. Petrov, \New methods in general relativity," Nau-ka, Moskow, 1966, 495 p. (in Russian).

[2] V.D. Zakharov, \Gravitational waves in the Einsteintheory of gravitation," Nauka, Moskow, 1972, 199 p.(in Russian).

[3] A.M. Baranov, Izv.Vuz.(Fizika), No.3, 73-78 (1995) (inRussian).

[4] D. Cramer, H. Shtefany, M.McCallum, E. Herlt,\Exact solutions of Einstein equations," Energoizdat,Moscow, 1982, p. 211-212 (in Russian).


Spacetime &SubstanceContents 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 AGGREGATERADIATION 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 ANDREPLICATION (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 CANDIDATESTO 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 INGRAVITATIONALMANEFF`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 RELATIVISTICASTROPHYSICS" (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 OFMEDIAL 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 COVARIANTLAGRANGIAN 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 OFGRAVITATIONAL 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 FORMODELS 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 Kiekh�oven. 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 MODELOF 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 THEORBITAL STABILITY OF THEMOTION PROB-LEMS IN GR (193).

M.M. Abdildin, M.E. Abishev. INTEGRATIONOF THE EQUATIONOF ROTATIONMOTION IN PROB-LEM 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 ELECTROMAG-NETISM IN NONLINEAR ELECTRODYNAMICS (199).

S.S. Sannikov-Proskurjakov, M.J.F.T. Cabbolet. RENORMALIZED NEWTONIAN CONCTANTAGAINSTEQUIVZLENCE 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 TESTINGIN 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 THEUNIVERSE (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 OFMISUNDERSTANDINGS (42).

Sergey Siparov. COSMIC MASER AS A REMOTE QUANTUM DETECTOR OF THE GRAVITATIONALWAVES: 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 COSMOLOGICALPROBLEMS (55).

W.B. Belayev. COSMOLOGICAL MODEL WITH MOVEMENT IN FIFTH DIMENSION (63).

L.C. Garcia de Andrade. METRIC AND DENSITY PERTURBATIONS IN WORMHOLE GEOMETRYWITH 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 INGENERALIZED SCALAR-TENSOR GRAVITIES (71).

V.L. Kalashnikov. X-MATTER INDUCED COSMOLOGICAL SCENARIOS IN THE RELATIVISTIC THE-ORY OF GRAVITY (75).

Jozef �Sima and Miroslav S�uken��k. BLACK HOLES | ESTIMATION OF THEIR LOWER AND UPPERMASS LIMITS STEMMING FROM THE MODEL OF EXPANSIVE NONDECELERATIVE UNIVERSE(79).

V.R. Kurbanova and A.B. Balakin. EXACTLY INTEGRABLE MODEL OF DYNAMICS OF VECTORBOSONS 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 UNI-VERSE (97).

B. Dragovich and Lj. Ne�si�c. ADELIC QUANTUM COSMOLOGY (100).

240 Contents of issues for 2000{2001 years

A.K. Mittal, Daksh Lohiya. CONDITIONAL COSMOLOGICAL PRINCIPLE AND FRACTAL COSMOL-OGY (104).

Alexandre Baranov and Dmitri Baranov. STATIC STAR MODEL AND MATHIEU FUNCTIONS (108).

H. Ch�avez, L. Masperi, M. Orsaria. SUPERHEAVY PARTICLES EITHER FOR UHECR OR FOR MUONANOMALY (111).

Jacques Moret-Bailly. POINTLESSNESS AND DANGEROUSNESS OF THE QUANTUM MECHANICS(116).

Miroslav S�uken��k and Jozef �Sima. PODKLETNOV'S PHENOMENON | GRAVITY ENHANCEMENTOR CESSATION? (124).

G.B. Alaverdyan, A.R. Harutyunyan, Yu.L. Vartanyan. ON SMALL MASS HYBRID STARS WITHQUARK 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 ASUBSTANCE (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 BINARYMODEL (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 OFTHE ETHER) (171).

N.A. Zhuck. ON THE UNITED NATURE OF GRAVITATIONAL, ELECTROMAGNETIC AND NUCLEARINTERACTIONS (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).

Spacetime &SubstanceInternational Physical Journal

INFORMATION FOR AUTHORS

The Editorial Council accepts the manuscripts for the publication only in an electronic variant in the formatfor LATEX 2.09. They should be completely prepared for the publication. The manuscripts are accepted by e-mailor on diskettes (3.5"). The manuscripts can be adopted in other view only for familiarization.

The original manuscripts should be preferably no longer then 6 pages. They should contain no more than 4�gures. Length of the manuscript can be up to 10 pages only in exclusive cases (at arguing problems of primaryimportance). If the length of the manuscript exceeds 10 pages, it should be divided by the author into two ormore papers, each of which should contain all pieces of a separate paper (title, authors, abstracts, text, referencesetc.). The Editorial Council accepts for the publication the brief reports too.

The payment for the publication of the manuscripts is not done. Each author gets the electronic version ofthat Journal edition, in which his paper was published free of charge.

An E-mail message acknowledging the receipt of the manuscript will be sent to the correspondingauthor within two working days after the manuscript receipt. If a message is not received please contact [email protected] to inquire about the manuscripts.

The Style File and Instructions for its use can be found at http://spacetime.narod.ru (sample.zip, 19 kb).An abstract (within 20 lines) must be submitted. This one should be concise and complete regardless of the

paper content. Include purpose, methodology, results, and conclusions. References should not be cited in theabstract. The abstract should be suitable for separate publication in an abstract journal and be adequate forindexing.

If the argument of an exponential is complicated or long, \exp" rather than \e" should be used. Awkwardfractional composition can be avoided by the proper introduction of negative degrees. Solidus fractions (l/r) shouldbe used, and enough enclosures should be included to avoid ambiguity in the text. According to the acceptedconvention, parentheses, brackets, and braces are in the order f [ ( ) ] g. Displayed equations should be numberedconsecutively throughout the paper; the number (in parentheses) should be to the right of the equation.

Figures (black-and-while) should be of minimal size providing clear understanding. Breadth of the �gure shouldnot exceed 84 mm or 174 mm (in exclusive cases). Figures should be made out as separate �les in the format of*.pcx (300 dpi/inch) or *.eps (minimum of kb).

Each �gure must be cited in numerical order in the text and must have �gure legend.Tables should be typed as authors expect them to look in print. Every table must have a title, and all columns

must have headings. Column headings must be arranged so that their relation to the data is clear. Footnotesshould be indicated by reference marks 1 , 2 etc. or by lowercase letters typed as superiors. Each table must becited in the text.

The Editorial Council accepts also response on papers, published in the Journal. They should be no more than1 journal page in length and should not contain �gures but only to refer to the already published materials. Butthey can contain the formulas. The recalls are publishing in section \Discussion."

The list of references may be formed either by �rst citation in the text, or alphabetically.Only works cited in the text should be included in the reference list. Personal communications and unpublished

data or reports are not included in the reference list; they should be shown parenthetically in the text: (F.S. Jones,unpublished data, 1990).

The title of paper is permissible not to indicate. It is permissible to give only the initial page number of apaper. The format of the reference list is as indicated below.

References

[1] F.W. Stecker, K.J. Frost, Nature, 245, 270 (1973).

[2] V.A. Brumberg, \Relativistic Celestial Mechanics", Nauka, Moskow, 1972 (in Russian).

[3] S.W. Hawking, in: \General Relativity. An Einstein Centenary Sutvey", eds. S.W. Hawking and W. Israel, Cambr.Univ. Press, Cambridge, England, 1979.

Read the Journal before sending a manuscript!

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

CONTENTS

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

Yu.M. Galaev. ETHERAL WIND IN EXPERIENCE OF MILLIMETRIC RADIOWAVESPROPAGATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

Alexandre Baranov and Michael Lukonenko. BROAD STATIC STARS CLASS MOD-ELLING WITHIN ONE APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

Alexandre Baranov and Sergei Tegai. ON FIXED SINGULARITIES IN KERR-SCHILDSPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

Alexandre Baranov and Nikolai Bardushko. ALGEBRAIC CLASSIFICATION OF 5DKRISHNA RAO WAVE SOLUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

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

Date post:	17-Nov-2020
Category:	Documents
Upload:	others
View:	0 times
Download:	0 times

ternational In ysical Ph Journal - orgonelab.org · UKR AI NE Kha rk i v Spacetime & Substance...

Documents