ternational In ysical Ph Journal - Orgone · U K R A I N E ISSN 1726-4499 Spacetime & Substance...

U K R A I N E ISSN 1726-4499

Spacetime &Substance

International Physical Journal

Volume 3, No. 5 (15), 2002

c 2002 Research and Technological Institute of

Transcription, Translation and Replication

JSC

U K R A I N E ISSN 1726-4499

Spacetime &SubstanceInternational Physical Journal

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Spacetime &Substance, Vol. 3 (2002), No. 5 (15), pp. 193{206c 2002 Research and Technological Institute of Transcription, Translation and Replication, JSC

EXPERIMENTAL EVIDENCE OF THE MICROWAVE

BACKGROUND RADIATION FORMATION THROUGH

THE THERMAL RADIATION OF METAGALAXY STARS

V.S. Troitskij, V.I. Aleshin1

Radiophysical Research Institute, N.Novgorod, Russia

Received Desember 2, 2002

The paper is devoted to the development of the theory of microwave background formation through the opti-cal radiation of Metagalaxy stars which is transformed due to the redshift into the microwave and infrared starbackground radiation. An application of the theory to the model of a stationary nonexpanding Universe of a sizenot less than 40{50 thousand Mpc shows that the star microwave background is not strictly the blackbody one.Its brightness temperature and spectral density correspond to 2:73K in Rayleigh-Jeans region of the background� > 1mm , but grow signi�cantly in submillimeter,infrared and optical wave ranges. This prediction is con�rmedby available measurements up to optical wavelengths. Besides, the value and dependence of small-space background uctuations on the angular resolution and the wavelength predicted by the theory is in a good agreement with theexperimental data. Finally, the fact, mysterious from the background relic origin point of view, of equality of thevolume background energy density and the optical star radiation energy has a very simple and natural explanation.An application of the theory to the closed model of the Universe in the big-bang cosmology shows that at wavelengths� > 1mm the star background is negligibly small (no more then 0.1K), but at submillimeter waves it signi�cantlyexceeds 2.7K that comes into con ict with the hypothesis of the background relic origin and the idea of the big bang.It follows from the results obtained that the observable nonblackbody electromagnetic background is not a relic oneand it has a star origin.

For majority opinion to change on the correctness of the hot big-bang cosmology, it is clear thatone or more of the arguments given above must be seen to fail ... . However, if a change doesoccur, it will probably come from one of three directions: ...b) A demonstration that there is an other plausible mechanism which could be responsible for theMBR, probably related to the idea that it does not have a perfect blackbody spectrum and/or thatit could not have been coupled to the matter at an earlier epoch (Burbidge, 1989, p. 988)

Introduction

The idea to explain the microwave background radia-tion by sources of di�erent nature is not new, but it hasnot yet been worked out in any concrete form.

In this paper we investigate a possibility to explainthe observed microwave background by the thermal ra-diation of the Metagalaxy stars. For this purpose it isevident to use some cosmological models of the struc-ture and evolution of the Universe. The problem ofthe contribution of the star integral radiation in stan-dard cosmology models was studied earlier. First stud-ies in this direction were carried out by McVittie(1962).On the methodical basis of this work Doroshkevich andNovikov(1964) have published only results of colcula-tions for di�erent models of the standard cosmology.

1e-mail: [email protected]

The methods of calculations were not given. It hasbeen shown, in particular, that at a wavelength of ob-servation �o > 1mm the volume energy density of thestar integral radiation is much less than the blackbodyradiation with the temperature T = 1K . There wasan a�rmation (Parijskij and Sunyaev 1973) that \theobserved relic radiation cannot be explained by the in-tegral radiation of discrete sources" in standard cosmol-ogy models. To calculate the radiation of galaxies, ascorrectly noted by Zel'dovich and Novikov (1967), \isof prime importance in a hot model since it is the back-ground on which the relic radiation of the model itselfis to be observed."

This is a valuable but unused so far test of thebackground relic origin theory. Recently there havebeen some serious experimental demonstrations thatthe standard cosmology does not re ect any more areal state of matter and radiation in the Universe (lu-

194 V.S. Troitskij, V.I. Aleshin

minosity of galaxies, their dimensions and evolution)(Segal 1992; Troitskij 1992,1994). In this connectionand due to existing alternative cosmological theories itbecomes important to explain the microwave by otherphysical reasons, in particular, by the optical radiationof stars in distant galaxies transformed into the radio-frequency band owing to the redshift of the radiationof stars along the path to an observer.

In this formulation the problem requires justi�edphysical procedures of calculation for its solution whichare absent in full measure so far. The method of calcu-lation and the �rst estimations presented earlier (Troit-skij 1994) had shown that in a static nonexpanding Uni-verse the 3K background can be explained by the ther-mal radiation of stars if the size of the stationary Uni-verse is at least by an order more than that of the gen-erally adopted. In this present paper we give a detailedphysical justi�cation of the calculation method whichis then applied to BGR calculation for di�erent modelsof the Universe including the standard one. A compar-ison is made for the results obtained for di�erent mod-els with the observed characteristics of the microwavebackground. This may a good test to choose this orthat theoretical model most adequate with the reality(see reviews of Baryshev 1992, Burbidge 1989). All saidabove justi�es the statement of the present work.

1. Physical basis of star microwavebackground formation

To determine this radiation let us consider the Uni-verse as the Euclidean space �lled with matter in theform of galaxies being the clusters of stars of di�erentspectral classes. We suppose that the spatial distri-bution of galaxies in the Metagalaxy space is uniformand isotropic and their mean parameters over a su�-ciently large volume do not depend practically on thedistance. We suggest as well the star thermal radia-tion as a blackbody one. At �rst let us consider thesolution of the problem in a simpli�ed form taking thetemperature of all stars equal in the whole galaxy. Letn gal=Mpc be the mean volume density of galaxies, m ,the mean number of stars in the galaxies, r , their meanradius, T ,the mean temperature of their photospheres.Let us take into account that the stars in galaxies arenot practically projected to which other.

Let us �nd the spectral power density of the ther-mal radiation ux from stars at radio frequency �0 inthe antenna aperture with reception diagram sterad.The full ux from the galaxies at metric distance R involume element R2 dR is

d� = F (�; T )�r2nmR2 dRd�: (1)

Here � is the radiation frequency of stars in theirown reference frame, F (�; T ) is the Plank's function

for the spectral density of the star blackbody emissivi-ty W=cm2Hz sr . Along the path of propagation up toa telescope antenna this radiation at frequency � willhave three types of attenuation and a frequency trans-formation due to the redshift. The �rst type is theattenuation in R2 times, the second type is the energyabsorption in the propagation medium which we shalldescribe by the function (R). And at last the thirdtype of attenuation is connected with the redshift of fre-quency � up to observation frequency �0 = �=(z + 1).To determine this type of attenuation there is no needto use any hypothesis on the redshift nature except thefact of its existence. Let us consider the star radiationwith a spectral density F (�T ) at frequency � in a nar-row frequency band d� . At the observation point allthis spectrum will be seen shifted down with boundary

frequencies � � 0:5��(z + 1)

and � + 0:5��(z + 1)

with unchanged

spectral density F (�0T ) since its increase in (z + 1)times due to the spectrum contraction is compensatedin the same times by weakening of the quantum ener-gy from h� to h�0 . Thus, the energy of the shiftedspectrum is equal to the integral of F (� T ) in band� �=(z + 1) i.e.

F (� T )��=(z + 1) = F (� T )� �0;

where � �0 = � �=(z + 1). This result is obtained aswell at a purely quantum approach. Indeed, radiationF (� T ) d� for very narrow band d� is a practically amonochromatic one and its power is proportional toh� . At the reception point this monochromatic radia-tion will have energy proportional to h�0 , i.e. less in(z + 1) times as compared with the radiated one. Thesame extinction will be as well in the case of a widereception band, overlapping all the spectrum of the ob-served radiation. To illustrate this point let us �nd thetotal energy received from the source with redshift z .As above, we suggest the source radiation in its frameof reference have Planck spectrum. In this case eachfrequency at the observer of the whole spectrum ex-tending from � = 0 to � !1 will have a shift to zerofrequency decreasing in (z + 1) times. This spectrumtake the form

d �0F (�0) =2h

c2�30(z + 1)3�

��exp

h�0(z + 1)

kT� 1

��1d�0; W=cm

2sr;

where �0 = �=(z + 1) is the frequency in the observ-er's reference frame. Integrating over all frequencies�0 from 0 to 1 and using the change of variablesh�0(z + 1)=kT = x we have an analogue of the Stefan-Boltzmann low

P =2�k4 T 4

h3c2(z + 1)

1Z0

x3

ex � 1dx = �T 4=(z + 1):

Experimental Evidence of the Microwave BackgroundRadiation Formation through the thermal radiation of Metagalaxy stars195

Thus, as it is expected all the energy received decreasesin (z + 1) times.

It should be noted that in the standard cosmologythe attenuation of galaxy radiation caused by the red-shift due to the Doppler e�ect is taken to be equal in(z + 1)2 times, i.e. for the Planck radiation spectrumF (� T ) d� the received signal has power

F (� T ) d�=(z + 1)2 = F (� T ) d�0=(z + 1):

This attenuation, as suggested, is due both to the de-crease of the quantum energy and their number (or inanother words the frequency band). It seems that inthis way the attenuation is determined twice: �rst in(z+1) times due to the decrease of the quantum ener-gy (quantum approach), and then again in (z+1) timesdue to the decrease of the band (classical approach), weconsider such an approach to be groundless.

So then, at the reception place we have the followingillumination from the considered volume element

dE = �r2 nm (R)�

�F [�0 (z + 1); T ] d�0dR; W=cm2sr; (2)

where F [�0(z + 1); T ] = 2h�30(z + 1)3=c2 [exp(h�0(z +1)=kT ) � 1]W=cm2sr Hz . The full illumination in theantenna aperture from all the galaxies in the solid angleof the radiotelescope antenna is

E = � r2 nmd�0

1Z0

F [�0(z + 1); T ] (R) dR: (3)

If (R) is such that at some R = Rmax; (Rmax) =0, then the upper limit of the integral will be de�niteand equal to Rmax . As it is obvious, at the given galaxydistance R its radiation at frequency � will come inthe reception band at the frequency �0 = �=(z + 1),if the galaxy redshift is z . In this way to integrateexpression (3) it is necessary to use the functional rela-tion between R and � or, ultimately, between R andz .

Then, substituting dR in (3) for dR = dRdz dz , (R)

for (z) we obtain �nally

E = �r2 nmd�0�

�zmZ0

F [�0(z + 1); T ] (z)dR

dzdz; W=cm2sr: (4)

In our case it is expedient to characterize the radia-tion E by the e�ective temperature Tb which is de�nedas a temperature of the blackbody radiation with thesame spectral power. Comparing (4) with the radiationof a black cavity

E = 2h�30 d�0=c2[exp(h�0=kTb)� 1]; W=cm2sr;

we obtain the required expression for the backgroundradiation temperature

� r2 nm2h�30c2

zmZ0

(z + 1)3 (R)dRdz dz

exp[h�0(z + 1)=kT ]� 1=

=2h�30

c2[exp (h�0=kTb) � 1]: (5)

The dimension of (5)is equal to W=cm2Hz sr . Indimensionless form designating �0 = c=�0 , where �0 isin meters, we have

� r2 nm

zmZ0

(z + 1)3 (R)dRdz dz

exphc(z + 1)=kT�0 � 1=

=

�exp

�hc

k�0Tb

�� 1

��1: (6)

Denoting the left part as x we have for the back-ground temperature

Tb(�0) =hc

k�0 ln[(x+ 1)=x]: (7)

Expression (6) is simpli�ed if, �rstly, in the up-per integration limit we have the condition hc(zm +1)=�0kT � 0:1�0:2 and, secondly, at the desired back-ground temperature Tb hc=�0kTb � 0:1� 0:2. As it is,taking the �rst term of the exponential function expan-sion we obtain from (6)

Tb = r2 nmT

zmZ0

(z + 1)2 (z)dR

dzdz: (8)

At zm = 3000 and T = 6 � 103K the �rst condition isful�lled for �0 � 3 cm and the second one at Tb � 3Kis ful�lled for �0 � 2:5 cm.

Now for integrating it is necessary to know R(z) inthe interval 0 � z � 1 . For this purpose one can usein the �rst approximation the Hubble law R = R0 zestablished experimentally for z � 0:02 or the lawR = R0

pz veri�ed by the observations of galaxies and

quasars in the interval 0 � z � 5 (Segal 1993, Troitskij1994). Then, for calculation it is necessary to deter-mine the attenuation function (R). This can be doneon the basis of di�erent physical grounds. At �rst wesuggest the simplest ones, namely, that beginning fromsome distance Rm the radiation from sources out fromregions R > Rm is completely screened (or absorbed)by the central parts of galaxies lying on the path ofwave propagation. This takes place when projectionsof all central parts of galaxies lying in the sight coneof length Rm are merging and taking area R2

m . Thenumber of galaxies in cone up to distance R is equalto N = nR3=3. The total projection area of their cen-tral parts of diameter 1 kPc is S = 0:25nR3l2 . This


area covers the part of the cross-section area of coneR2 . Hence, only a part of radiation will pass throughthe cross-section (R) = 1�0:25Rnl2 . The channel willbe fully closed when = 0, i.e. at Rm = 1=0:25nl2 ,then (R) = 1 � R=Rm or at R = R0

pz we have

(z) = 1�pz=zm . Here the attenuation (or screening)function does not depend on the wavelength that takesplace practically for the optical radiation forming theobserved background. Let us take for the calculationl = 6 kPc; n = 2, then Rm ' 50000MPc; zm ' 6 103 .

In the given estimation the galaxies and the starsinside the galaxies are regarded immovable relative thegiven spherical coordinate system with a centre at theobserver. In reality there exist proper motions of thegalaxies as well as the stars inside them. It is obviousthat the account of these motions does not change theresult obtained. Indeed, in a su�ciently large volume,say ' 103MPc , containing several thousand galax-ies the directions of motions are distributed isotropi-cally and the velocity values are distributed accordingto the normal law with the rms velocity � 300km=s .So, the radiation of galaxies will have the frequencyshift not more than ��=� ' �v=c ' 10�3: Owing tothis fact the observed radiation temperature from eachgalaxy well di�er from the average one not more than�T=T � � 10�3 . Due smallness of the e�ect and itshomogeneity when adding radiation of a large numberof galaxies, the in uence of this chaotic velocities on theradiation frequency and temperature will be mutuallycompensated. The same can be said on the in uenceof the velocity dispersion of the galaxy stars. Thus,the uniform and isotropic microwave background �xesin a statistical sense the immovable coordinate systemresting on all the galaxies of the visible part of the Uni-verse.

2. Jeneral expression for starmicrowave background radiation ofthe Metagalaxy

In this section we give quite a general expression forthe star background suitable for di�erent models of theUniverse. We suggest space �lling with the galaxies beuniform and isotropic and their mean luminosity anddimensions be invariant in time and space. The prob-lem is to give a calculation taking into account a con-tribution of the stars of di�erent spectral classes, i.e.with di�erent photosphere temperatures and sizes. Asit is known, more than 80 per cent of stars in galax-ies are those of the main sequence and hence they willdetermine chie y the observed star background. Forthis stars the required parameters r and T are giventhrough the star luminosity M , determining its spec-tral class, radius and photosphere temperature. Let ususe the known formula for the relative stellar radius

r=r�

lg r=r� =5000

T� 0:2M � 0:02; (9)

where T is the photospheric temperature of the starand M is its photographic value. The relation MT isusually given in tables and for the stars of the mainsequence it is approximated with a su�cient accuracyby the function

T =26 103

0:37M + 2:4: (10)

Substituting (10) into (9) we have

r2

r2�= 10�0:233M+1:05: (11)

The luminosity distribution of the main sequencestars '(M ) has been known (see, for example Lang1974). The luminosity function '(M ) is given in thetable form in the interval M � 1

2near the integer value

from M = �4 to M = 20 that involves spectral class-es B AF GKM: The intervals of M values of thesespectral classes are equal respectively to (-4,-1), (0,+3),(+4,+6), (+7,+9), (+10,+19). We have used normal-ization

P'(M ) = 1. As a result, the full radiation

will be

� r2�nm19X�4

10�0;233M+1;05'(M )�

�zmZ0

(z + 1)3 (z)dRdz dz

expfhc(z + 1)=�0kTg � 1=

=

�exp

hc

k�0Tb� 1

��1: (12)

Here T is de�ned by (10). Function dR=dz is deter-mined by accepted theoretical or experimental depen-dence R(z). Expression (12) does not depend explicitlyon the accepted nature of the redshift. Its nature man-ifests only through concrete functions R(z). For theexperimental model of the Universe R(z) = R0

pz , for

the closed model of the standard cosmology R(z) =cH�1z=(z + 1) and so on.

3. Star microwave backgroundradiation in a static model of theUniverse

We consider the static model of the Universe. Space �ll-ing with the galaxies is uniform and isotropic in scalesestimated by contemporary observations. We also sug-gest the mean dimensions and luminosity in the samescales to be invariant in time and in the whole Meta-galaxy space. It is essential that this model follows


from observed mean (statistical) dependences of appar-ent luminosity m(z) and angular dimensions �(z) ofthe galaxies and quasars which make possible to de-termine the really existing dependence R(z) equal toR = 600

pzMpc in the redshift interval 0 � z � 5

(Troitskij 1995). Taking into account in (12), thatR = R0

pz , where R0 = 600Mpc we have

A19X�4

10�0:233M+1:05'(M )�

�zmZ0

z�1=2(z + 1)3 (z)dz


=

�exp

hc

k�0Tb� 1

��1: (13)

Here T is given by (10), A = 12�r2� nmR0 .

Parameter A may have only admissible limits ofpossible values since a strict mean value of nm , i.e.a star number in a cubic Mpc, is unknown. Accord-ing to the data on the population of the Local Groupcontaining three large galaxies with the star numberm = 1011�1012 and about two tens with the star num-ber one-one and a half orders less one can take 1010 �nm � 1011 . Then at R0 = 600Mpc admissible value ofA lies in the interval 10�12 � A � 10�10 , which maybe used in the background calculation. Then taking themean size of the central part of galaxies l ' 6Kpc wehave (z) = 1�pz=zm , where zm � 5000� 7000.

The calculation results of the background tempera-ture are given in Tables 1 and 2 in the waveband from1m to parts of a micron. The �rst table has been cal-culated for the law R = R0

pz , the second one for the

Hubble linear law R = RH z extrapolated beyond thelimits of its experimental grounding within the inter-val 0 � z � 0:02. The comparison of two tables showsthere is not any signi�cant di�erence in the backgroundtemperature dependence on wavelength. It can be seenfrom the tables that at waves � > 1mm the backgroundis determined by the stars of spectral classes AF G , at� < 1mm by those of classes BA and in the ultravio-let by only those of class B . To check these results wemade as well the calculation of the background attenu-ation in (z +1)2 times due to the redshift. In this casethe dependencies remain practically unchanged, but thevalue of A is an order higher than that as an upper limitestimate both for two laws R = R0

pz and the Hubble

one.A most interesting and unexpected result of the the-

ory is the growth of the background temperature in thesubmillimetre waveband. Any reasonable attempts toeliminate this growth were failed. Finally, it has beenunderstood that the growth aries due to a sharp di�er-ence of the star background from the blackbody oneat submillimetre and shorter wavelengths. This has

Figure 1: A comparison of the star background spectrumfor the universe static model (solid line at zm = 5 � 103 � 7 �105 ) with the blackbody spectrum at Tb = 2:73K (dottedline)

been shown in Fig. 1 where the star background spec-trum is given in comparison with the blackbody oneat T = 2:7K . Theoretical and blackbody spectra atT = 2:7K coincide in the Rayleigh-Jean's region of thePlanck's spectrum and sharply di�er in the Wiens's re-gion at � < 1mm . Here the star spectrum is practically at and its spectral density exceeds the spectral densityof the Planck's spectrum by many orders at T = 2:7Kthat causes the growth of the equivalent backgroundtemperature. The reason of the spectra di�erence isthe fact that the star background is added up basical-ly from the Rayleigh-Jeans's parts of the star radiationspectra which extend to optical frequencies at a highstar temperature. Really, the integral in (13)decreasesexponentially with the frequency and, hence, beginningwith some value of z it does not give any essentionalcontribution in integral (13). One may conclude thatthis takes place when hc(z + 1)=k�0T and the expres-sion hc(z+1)=k�0T = 1 determines at the given valuesof T and �0 an actual upper limit of integration. Asa result, each spectral class of stars for di�erent obser-vational waves has its actual upper limit of integrationover z related as it is obvious with the cuto� of thestar Planck's spectrum in its Wiens's region. Thus, thebackground radiation is basically made at the star ra-diation in the Rayleigh-Jeans's region. Table III givesthe values of zef , characterizes the size of galactic lay-er R = R0

pzef responsible chie y for the observed

background radiation at a given wavelength. It is seenfrom the table, that at centimeter and longer waves� > (0:5 � 1)cmthe background spectrum intensity isbounded by galaxy screening at zm � (5� 7) � 103 andat � � 0:1 cm by the cuto� of the star radiation in-tensity in the Wiens's spectrum region. As a result,


the background radiation in the Wiens's region is deter-mined by rather a thin layer of galaxies radiations in theRayleigh-Jeans's region of the spectrum. The reductionin number of galaxies responsible for the background at� � 1mm is an important factor which leads to an es-sential increase of small-scale background uctuationsfor shorter waves, that is con�rmed by observations.

When calculating the star background we studiedhow the background temperature is in uenced by anincrease of the star photosphere temperature at wave-lengths longer than 1cm. To estimate this in uence wehave the only example, the Sun. Its brightness temper-ature for �0 � 1m may be approximately expressed bythe relation T = T0 + 5 � 105� , where � = �0=(z + 1)in meters. At such temperature of stars Tb increases atwaves �0 � 20cm no more than 0:01K . At last, as faras, the calculation procedure is concerned, it should beremembered that the background temperature is de-termined by two values A and zm . On the basis ofabove mentioned calculations of the limit visibility zmwas taken as an initial value and a strict value of A isdetermined from a requirement that at �0 = 3cm thebackground temperature should be 2.73K. This value ofA is given in tables. It is clear, only those calculationswere used where A did not exceed the limits mentionedabove.

4. A comparison of predictions of thestar background radiation theorywith the measurements

Up to now extensive background measurements havebeen carried up to far IR close to optics. The starbackground theory may appear to be actual up to op-tical waves, so the comparison is not to be bound withthe submillimetre waveband. Besides, the theory pro-posed explains naturally the observed small-scale space uctuations of the background intensity as well as amysterious so far phenomenon of the equality of themicrowave background intensity and the optical radia-tion of a mean galaxy including ours. These questionsare considered in detail below.

4.1. The star background spectrum andobservations

Its obvious, that the comparison of the theory with ob-servations is of interest �rst of all in the submillime-tre waveband. The background measurements in thiswavelength region have already been in progress for aquarter of a century. They have been started to con-�rm the blackbody character of radiation at this wavesfollowed from the Big Bang theory. �rst investigationsat wavelengths �0 < 1mm carried out by three inde-pendent laboratories of the USA on the high-altitudeballoons and satellite gave contradictory results: some

Figure 2: Theoretical dependence of the star backgroundtemperature on the wavelength for the static model of theuniverse at zm = (5 � 7) � 103 as compared with the mea-surement data (crosses)

got values Tb = 2:7K , the others after correction to de-crease got Tb = (3:6�5:5)K (see review of Bliter 1974).Note, the measurements giving a higher temperaturethen 2:7K were and are being questioned since theycontradict the standard cosmology theory. However,the data mentioned have last their meaning because ofuncertainty in the value of the observation wavelengthdue to a wide band comparable with the mean frequen-cy of reception.

At present there have been reliable results in thework of Matsumoto (1988) at wavelengths 1.16, 0.7,0.48, 0.137 and 0.1 mm the accuracy of which is notworse than (3-5)%. According to the IRAS (infraredastronomical satellite) program the background mea-surements have been carried out at 0.1 mm and 0.6mm, they have been presented in Matsomoto's pa-per after correction. Most of these results are giv-en in ux units W=cm2:sr:Hz with exception of da-ta at 1.16, 0.7 and 0.48 mm for which there havebeen the background brightness temperatures as well.The values of the background temperatures for rest ofthe waves have been calculated according to relationB(�) = 2h�30=c

2(exph�=kTb�1), where B(�) | is themeasured radiation ux in W=cm2srHz . A test cal-culation of the temperature for three above mentionedwaves have proved the correctness of the temperaturecalculation by this relation for other uxes.

Recently the measurements of the cosmic microwavebackground were carried out by satellite COBE (Cos-mic Background Explorer) with a help of receiver FI-RAS (Far-Infrared Absolute Spectrometer) in the wave-length band 0.5-5 mm (Mather, et al 1994). The back-ground temperature in this continuous band have beenfound to be equal to Tb = 2:726� 0:01K . The satellite


COBE was also used according to the Program DIRBE(Di�uz Infra Red Background Experiment) to get up-per limits of background values in the direction of thesouth ecliptic pole at wavelengths 240, 143, 100 and 60�m (Kowada, et al. 1994). There have also been thevalue of the background upper limit at � = 154�m . Wehave used as well the review of the background measure-ments at radio wavelengths (Kogut, et al. 1988). Fi-nally,to make the picture of the background spectrumfull we ventured to use data at 0:3 � 0:8�m (Leinert,et al. 1995; Lang 1974) and in the ultraviolet at 912angstrom (Vikhlinin 1995). All this mentioned datahave been tabulated in Table IV in units of the spectral ux density and brightness temperature. Fig. 2 givesa comparison of these data with the theoretical expres-sion of the background spectrum and Fig. 3 comparesthem with the background brightness temperature de-pendence on the wavelength. As it is seen from �gures,the theoretical dependencies are quite well con�rmedby the experimental data not only at IR but also inoptics and the ultraviolet. This is an absolutely sud-den result.Some divergence for Tb(�) can be seen inthe submillimetre wavebaund. We think this may be aconsequence of a systematic error of the measurementswhich authors had been experiencing a quite naturalsubconscious pressure of theoretical prejudices. How-ever, we should note that this divergence is eliminatedeither by an account of nonblackbodiness of the starradiation in the Wien's region or by an account of in-tergalactic absorption of optical waves or at last by asmall reduction in estimates of a relative number ofbrightest stars in class B. The value 0:15% given inliterature and used by ours may be overestimated dueto the observational selection. Finally, it must alwaysbe kept in mind that the background measurements atwavelengths shorter than 0.5mm are aggravated by apossible impact of the interplanetary and interstar dustradiation. Some hypotheses given in the literature re-port that the observed background at � � 0:1mm isdetermined to a great extent by the dust at T ' 20Kand so on. The uncertainty of corrections of this radi-ation explains naturally a large spread of the data on uxes of the cosmic origin. However, despite this fact,one can de�nitely conclude that the experimental datain a wide wave interval do not con�rm the hypothesis ofthe background relic origin and are in a good agreementwith the background star theory.

Recently the background measurements have beenmade by the population of levels of the hyper�ne struc-ture at mm waves in carbon clouds with the redshiftsz = 1:776 and z = 2:9 being near quasars. In the �rstcase the �rst level of the carbon hyper�ne structurehas been used and the temperature Tb(1:7) = 13:5Khas ben obtained (Songaila, et al. 1994). This result�ts formally the Big Bang theory which gives Tb(z) =2:73(z + 1). However, to explain these experiments wecannot exclude possible energy pumping from a neigh-

Figure 3: Theoretical spectrum of the star background atzm = (5� 7) � 103 as compared with the measurement data(crosses)

boring quasar (in the �rst case quasar Q1331+1700),so these data were not included in Table IV.

In conclusion one cannot but note an extraodinarystability of the calculated background spectra to thealterations of the calculation parameters A;'(M ); zmand its dependence on the wavelength zm(�) and soforth. It even tuned out that the spectrum was notpractically changed if we had used a simpli�ed expres-sion (6) for stars of classes FG.

4.2. A mysterious equality of the backgroundenergy density and the optical radiationenergy of our Galaxy stars has a simpleexplanation

As it is seen from (2-4) the radiation received byradiotelescopes in a su�ciently narrow band d�0 isformed from the radiation of galaxies disposed at dif-ferent distances R along the line of sight. Each galaxycontributes therewith only at a frequency correspond-ing to its distance, i.e. �(R) = �0(z + 1). No otherradiation of the galaxy emitted at other frequencies ofits spectrum is received by the radiotelescope tuned atfrequency �0 . If the galaxies have the Planck's radia-tion spectrum each galaxy contribution is determinedby the Planck's function at frequency �(R) and is equalto F [�(R); T d�0] . It is also seen from (2)-(4) that thesignal at frequency �0 is added up from equal e�ectivenumber of galaxies for each interval. This takes placeobviously because the number of galaxies in each inter-val R growths as nR2 dR and their radiation energyat the observer decreases in R2 times and, hence, isproportional to n dR , i.e. does not depend on dis-tance but only on dR . In doing so we can choose dR insuch a way as to have only one galaxy in each interval.


It results that each galaxy in the line of sight would bea lantern of a monochromatic optical radiation of dif-ferent colors of the Planck's spectrum. However, fromthe observer's point of view (he is tuned on frequency�0 ) they are one-color radiators at frequency �0 placednear the observer. As a result, the contribution of allthe galaxies in the radiation received at frequency �0will be equal to the sum of all radiations at all fre-quencies of the Planck's spectrum from one galaxy. Itfollows immediately according to (2-6) that the back-ground energy ux is simply equal to the integral overfrequency energy ux of the optical radiation of onemean galaxy.

The equality of the blackground energy density andthe radiation density of the stars of our Galaxy wasdiscovered more than 15 years ago and was a serioustheoretical problem not being solved in the model ofthe background relic origin. Contrary to this, this factfollows naturally from the theory of the backgroundstar origin in a boundness stationary and uniform overall mean parameters Universe. Below we give the cor-responding calculations for the volume density of thestar background energy.

Expression (5) gives the value of the observed radi-ation ux spectral density. Multiplying it by d�0 and4=c and integrating over frequency �0 from zero to in-�nity we obtain the following expression for the volumedensity of the background energy

� r2nm

1Z0

8h�30c3

d�0

zmZ0

(z + 1)3 (z) dR

exph�0(z + 1)=kT � 1=

=

1Z0

8�30h

c3d�0

exph�0=kTb � 1=

4

c�T 4

b : (14)

At Tb = 2:7K the right part gives the radiation volumedensity �b = 0:24 ev=cm3. Now let us calculate theradiation volume density of the stars of our Galaxy. Asit is obvious we should take herewith in (14) z = 0 andthe mean star density nm equal to m=0:5 l3 , where l isa mean diameter of the Galaxy.

�� =2r2m

l2

1Z�0

8�h�30 d�0c3(exp h�0=kT � 1)

=

=

�2r2m

l2

�T 4

T 4b

��4

c�T 4

b

For t = 6000K , l = 15 kPc, m = 1010 , Tb = 2:7Kthe value in square brackets is close to unit and, hence,�� ' 4

c�T4b = �b = 0:24 ev=m3 Thus the approximate

equality of the volume densities of the microwave back-ground energy and the optical radiation of our Galaxyis explained by the identity of the nature of the back-ground and the star optical radiation and as well by the

Figure 4: The measurement results of the small-scalespace uctuations of the background temperature �T=Tas a function of the radiotelescope antenna pattern widthin minutes of arc: |the measurement of Parijskij; 2 |the measurements of Berlin. Solid line | the theoreticalcurve

fact that our Galaxy is close to the mean statistical one.Naturally, this coincidence could not be explained fromthe point of view of the background relic origin,thatwas specially noted in the review of Burbidge (1989).

4.3. Background small-scale anisotropy

The spatial variations of the background radiation in-tensity are determined by a change of x(�) of integral(6) as dependent on direction � of the antenna. In thisway according to (7)

Tb(�) = hc=k�0 ln

�1 +

1

x

�:

Usually x�1 >> 1 and �Tb=Tb(�) = �x=x . Then we�nd a derivative of logx in (6) and obtain �x=x =2�r=r+�n=n+�m=m , here �r; �n; �m are dis-persions of corresponding values. The value r is a meandimension, so �r ' 0. The dispersion of the numberof stars in galaxies , as it is known, is

pm .

To determine the dispersion of n it is necessary toaccount the total number of galaxies in the antenna pat-tern up to the e�ective distance of visibility Re(�) �Rm depending on � according to Table III. In the an-tenna �eld of sight equal to sterad there will beN = n 0:33R(�)3 galaxies with dispersion �N =pN =

pn 0:33R(�)3. Then �n = �N=0:33R3

e(�)and n = N=0:33R3

e(�) from where �n=n = �N=N =1=p0:33nR(�)3. Due to independence of random

variables n and m �T=T =p(�n=n)2 + (�m=m)2


Figure 5: Experimental dependence of �T=T as a func-tion of observation of wavelength

and we have �nally

�T

T=

1pm

p1 +m=0:33nR(�)3: (15)

The measurement results of background tempera-ture uctuations have been given in the review of Par-ijskij (1990). These results are shown in Fig. 4 in theform of the dependence of lg�T=T on lg in the in-terval 0 < � 2, containing 73 data points. Themeasurement of �T=T were carried out in the wave-length interval 10�1 � �0 � 50 cm at a di�erent widthof the antenna pattern 0:020 � p � 30000:

All measurement results are within interval 10�5 ��T=T � 10�3 . It is not possible to reveal any regularbehavior in the dependence of �T=T on over all datagiven in Fig. 4 due to a strong spread of data composedof measurement of di�erent authors and measurementprocedures. However, we hope that the data of thesame authors for di�erent are most free of relativeerrors. These data are those of Parijskij and Berlin.According to the data of these authors in Fig. 4 wehave clear dependencies of �T=T on . Here as wellthere has been at he theoretical dependence calculatedfor n = 2, m = 1010 and Re(�) = 40 � 103Mpc validfor �0 > 1mm which as is seen well agrees with the ex-perimental data of Parijskij and Berlin. Thus, the ob-served small-scale background anisotropy is explainedby discreteness of the background radiation sources, thegalaxy stars. Besides, the calculation presented pre-dicts according to (15) and Table III the dependence of�T=T on the observation wave through the change ofthe size of the galaxy e�ective layer taking part in thebackground formation. To reveal this dependence oneshould exclude the in uence of . For this purpose wehave sampled the measurement from the data of Fig.4 in a su�ciently narrow band 0:8 � lg � 1:2 andthen have plotted the dependence �T=T on � . Fig.

Figure 6: Spatial dependence of the value X =[(�T=T )2 �m�1] on the wavelength (solid line) as com-pared with the experimental data of TableIV (points)

5 presents this dependence which con�rms the predic-tion. The desired dependence was determined as wellfrom all the data. One can obtain easily from (15) thedependence excluding the in uence of , namely

X =

"��T

T

�2� 1

m

# =

m

0:33nR3(�):

Here �T=T and are the corresponding experimentaldata from Fig. 4. Fig. 6 gives the experimental depen-dence of X on � in comparison with the th theoreticalone. The fact of their proper coincidence is a strongargument in favor of the theory of the star backgroundformation.

5. Star microwave background in thestandard cosmology model and inthe alternative theories

For general formula (12) will do to calculate the back-ground in this case. A speci�c point for the standardcosmologymodels is a restriction of the integration lim-it in (12) up to zm < 10 owing to a limited existencetime of the galaxies. In the process of calculation for theclosed model we have to take the theoretical expressionfor the distance-redshift relation R(z) = cH�1

0 z=(z+1),where cH�1

0 = RH is the Universe radius. In this casedR=dz = RH=(z + 1)2 and the general expression (12)has the following form

AH

19X�4

10�0:233M+1:05'(M )�

�10Z0

(z + 1) (z)dz



=

�exp

hc

kTb�0� 1

��1; (16)

where AH = � r2�nmcH�10 . Let us take H0 = 75

km=sMpc and (z) = 1.Table V gives the calculation result at the mini-

mum value of A for two values of zm = 5 and 10from where it is seen that the star background temper-ature exceeds 2:7K at submillimetre waves and makesits noticeable part at millimetre waves. From that itfollows an unambiguous conclusion that the observedmicrowave background is to be consisted of the sum ofstar and relic contributions. In other words the relicbackground has no place at millimetre and especiallysubmillimetre waves. Hence, we have a de�nite incon-sistency of the Big Bang theory to explain the observedmicrowave background radiation.

From the given calculation it is clear that none ofthe models with a hot origin can explain the microwavebackground by the optical radiation of stars. In thiscase the existence region of the galaxies form is get-ting too small limited by the interval z � 10. Herewe include the in ation model and the models basedon conformal metrics (Hoyle and Narlikar 1972, Troit-skij 1987, Petit 1988). The models of a steady-state,i.e. nonexpanding, nonlimited in space and time Uni-verse are in a particular position. We have here themodel which explains the redshift by \quantum aging."In this case, as it is known, the quantum energy issupposed to have an exponential attenuation with dis-tance, that gives R = R0 ln(z + 1). Here observationbackground is also explained by the optical radiation ofstars. In conclusion we have to note, that microwavebackground distortions associated with the interactionof relativistic electrons with photons etc. considered indetail by Sel'dovich and Sunyaev (1992) are also validin the model of the background star origin.

6. Conclusion

All observatiounal imlications of the MBR star origintheory of the stationary nonlimited in space and timeUniverse are con�rmed by all known experimental data.The theoretical background spectrum obtained is con-�rmed by experimental data in a wide band from deci-metric to IR and, probably, even to optical waves. Thisdemonstrates a plausible mechanism of the backgroundformation resulting in a conclusion that MBR is nota perfect blackbody radiation and cannot be coupledto the matter at a earlier epoch. An additional factorof trust is the explanation of a mysterious equality ofthe MBR energy density and the optical radiation en-ergy density of stars in our Galaxy, as well as the causeof background small-scale anisotropy which predict val-ue and dependence on the antenna pattern width andobservation wavelength are con�rmed by the measure-

ments. All this is a serious evidence against the ideaof Big Bang and in favor of the steady-state Universehypothesis.

References

[1] Yu.V. Baryshev. \Progress of Science and Technolo-gy," Gravitation and Cosmology, 4 (1992), (Moscow, inRussian).

[2] A.D. Bliter. IAU Symposium N63: \Conformation ofCosmological Theories with Observational Data," 1974(USA).

[3] G.R. Burbidge. Int. J. Theor. Phys., 28, 983 (1989).

[4] A.G. Doroshkevich, I.D. Novikov. DAN USSR, 154,809 (1964).

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[10] J.C. Mather, E.S. Cheng, D.A. Cottengham. Ap. J.,420, 439 (1994).

[11] T. Matsumoto, H. Hayakawa, H. Matsyo et al. Ap. J.329, 567 (1988).

[12] G.C. McVittie. Phys. Rev. 128, 2871 (1962).

[13] Yu.N.. Parijskij and D.V. Korol'kov. Progress of Sci-ence and Technology. Astronomy, 31, 73 (1986).

[14] Yu.N. Parijskij and R.A. Sunyaev. IAU SymposiumN63: \Confrontation of Cosmological Theories withObservational Data," 1974 (USA).

[15] J.P. Petit. Modern Physics Letters A. 3, 1527 (1988).

[16] E. Segal. Proc. Natl. Acad. Sci. USA 90, 4798 (1993).

[17] A. Songaila, L. Cowre, C. Hogan, M. Bugers. Nature,368, 599 (1994).

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Table I

The star background radiation in the static model of the universe at R=R0 z1=2 for di�erent combinations of parametersA and zm . Columns 2-6 are the relative contributions of the stars of spectral classes B A F G K M into the background

radiation. The �rst line of the columns 2-6 is a relative number of the stars of the given class.

A = 0.11488E - 10 MAX Z= 7000.0

�(mm) B/S A/S FG/S K/S M/S T back

0.013% 1.40% 7.47% 9.29% 81.82%0.0001 0.986 0.014 0.000 0.000 0.000 3668.360.001 0.219 0.560 0.195 0.023 0.003 520.080.010 0.238 0.543 0.189 0.025 0.005 71.950.100 0.231 0.547 0.191 0.025 0.005 11.881.000 0.165 0.568 0.228 0.032 0.006 3.0910.000 0.061 0.480 0.358 0.075 0.025 2.5630.000 0.053 0.454 0.373 0.086 0.034 2.73100.000 0.050 0.445 0.378 0.090 0.037 2.81200.000 0.050 0.443 0.379 0.090 0.038 2.83400.000 0.050 0.442 0.379 0.091 0.039 2.84800.000 0.049 0.442 0.379 0.091 0.039 2.85700.000 0.049 0.442 0.379 0.091 0.039 2.851000.000 0.049 0.441 0.379 0.091 0.039 2.85

A = 0.25633E -10 MAX Z = 5000.0


0.013% 1.40% 7.47% 9.29% 81.82%0.0001 0.986 0.014 0.000 0.000 0.000 3740.040.001 0.220 0.560 0.193 0.023 0.003 535.290.010 0.237 0.543 0.190 0.025 0.005 74.920.100 0.228 0.549 0.193 0.026 0.005 12.681.000 0.141 0.570 0.245 0.036 0.007 3.5310.000 0.057 0.469 0.365 0.080 0.028 2.7230.000 0.052 0.450 0.375 0.087 0.035 2.73100.000 0.050 0.444 0.378 0.090 0.038 2.74200.000 0.050 0.442 0.379 0.091 0.038 2.74400.000 0.049 0.442 0.379 0.091 0.039 2.74800.000 0.049 0.441 0.379 0.091 0.039 2.75700.000 0.049 0.441 0.379 0.091 0.039 2.751000.000 0.049 0.441 0.379 0.091 0.039 2.75

A=0.88421E - 10 MAX Z = 3000.0


0.013% 1.40% 7.47% 9.29% 81.82%0.0001 0.986 0.014 0.000 0.000 0.000 3857.520.001 0.222 0.561 0.191 0.023 0.003 560.660.010 0.235 0.544 0.191 0.025 0.005 80.000.100 0.220 0.551 0.197 0.026 0.005 14.131.000 0.108 0.558 0.281 0.044 0.010 4.3110.000 0.054 0.458 0.371 0.084 0.032 2.8930.000 0.051 0.447 0.377 0.089 0.037 2.73100.000 0.050 0.443 0.379 0.090 0.038 2.67200.000 0.050 0.442 0.379 0.091 0.039 2.66400.000 0.049 0.441 0.379 0.091 0.039 2.65800.000 0.049 0.441 0.379 0.091 0.039 2.65700.000 0.049 0.441 0.379 0.091 0.039 2.651000.000 0.049 0.441 0.380 0.091 0.039 2.65


Table II

The same as in Table I, but for the Hubble law R=RH * z.

A = 0.11362E - 11 MAX Z=3000.0


0.013% 1.40% 7.47% 9.29% 81.82%0.0001 0.994 0.006 0.000 0.000 0.000 3381.340.001 0.350 0.517 0.121 0.011 0.001 488.630.010 0.313 0.520 0.147 0.017 0.003 71.290.100 0.285 0.535 0.159 0.019 0.003 12.821.000 0.119 0.573 0.263 0.038 0.007 4.0910.000 0.055 0.460 0.370 0.084 0.032 2.8630.000 0.051 0.447 0.377 0.089 0.037 2.73100.000 0.050 0.443 0.379 0.090 0.038 2.68200.000 0.050 0.442 0.379 0.091 0.039 2.67400.000 0.049 0.441 0.379 0.091 0.039 2.66800.000 0.049 0.441 0.379 0.091 0.039 2.66700.000 0.049 0.441 0.379 0.091 0.039 2.66100.000 0.049 0.441 0.380 0.091 0.039 2.66

A = 0.25601E - 11 MAX 2=5000.0


0.013% 1.40% 7.47% 9.29% 81.82%0.0001 0.994 0.006 0.000 0.000 0.000 3264.100.001 0.351 0.516 0.120 0.011 0.001 465.140.010 0.315 0.519 0.146 0.017 0.003 66.450.100 0.296 0.529 0.154 0.018 0.003 11.401.000 0.166 0.582 0.218 0.029 0.005 3.2810.000 0.058 0.472 0.364 0.079 0.028 2.6830.000 0.052 0.451 0.375 0.087 0.035 2.73100.000 0.050 0.444 0.378 0.090 0.038 2.76200.000 0.050 0.443 0.379 0.090 0.038 2.76400.000 0.050 0.442 0.379 0.091 0.039 2.77800.000 0.049 0.441 0.379 0.091 0.039 2.77700.000 0.049 0.441 0.379 0.091 0.039 2.771000.000 0.049 0.441 0.379 0.091 0.039 2.77

Table III

The dependence of the e�ective distance of di�erent spectral class on the observation wavelength.

�0cm

T = 25�103

ZeT = 10�103

ZeT = 6�103

ZeT = 4�103

Ze10 175�103 70�103 42�103 28�103

1 17.5�103 7.103 4.2�103 2.8�103

0.1 1750 700 420 2800.01 175 70 42 280.001 17.5 7 4.2 2.80.0001 1.75 0.7 0.42 0.28


Table IV

Experimental measurement data of the background radiation spectral density and its brightness temperature asdependent on wavelength. 1-16 - Kogut 1988, 17-18 - Meyer 1986, 19-24 - Matsumoto 1988, 25-36 - Mather 1994, 37-43 -

Kawada 1994, 44-46 - Leinert 1995, 47 - Lang 1974, 48 -Vikhlinin 1995.

No � [mm]B(�)�10�24

WTb [

oK] No � [mm]B(�)�10�24

WTb [

oK]

cm2�sr�Hz cm2�sr�Hz1 120.000 0.522 2.780 25 350.000 0.060 2.7002 81.000 1.049 2.580 26 125.000 0.467 2.7003 63.000 1.801 2.700 27 80.000 1.105 2.6504 30.000 7.297 2.610 28 70.000 1.465 2.7005 12.000 42.655 2.780 29 40.000 4.254 2.6406 9.090 69.962 2.810 30 10.000 59.173 2.8007 3.330 252.266 2.600 31 5.000 169.739 2.7268 2.640 331.158 2.700 32 4.000 226.599 2.7269 2.640 342.627 2.740 33 3.000 306.290 2.72610 1.320 340.065 2.760 34 2.000 382.538 2.72611 1.320 335.124 2.750 35 1.000 204.305 2.72612 3.510 276.694 2.800 36 0.500 8.321 2.72613 1.980 477.012 2.950 37 0.240 5.600 7.01314 1.480 456.029 2.920 38 0.154 1.330 5.86715 1.140 231.624 2.650 39 0.134 5.800 7.22116 1.000 141.735 2.550 40 0.130 4.800 7.30517 2.640 339.750 2.730 41 0.100 3.300 8.82018 1.320 360.202 2.800 42 0.095 5.000 9.43619 1.160 302.769 2.790 43 0.060 4.800 13.72620 0.709 116.866 2.956 44 0.0008 0.650 554.56021 0.481 29.404 3.179 45 0.00035 0.135 1126.72222 0.262 3.678 4.125 46 0.0005 0.250 826.94523 0.137 82.966 8.650 47 0.00065 0.450 662.29424 0.102 3.700 8.740 48 0.00000912 0.0001 3181.021

Table V

The star component of the background for the closed model of the universe in the standard cosmology.

A = 0.15000 E-11 MAX Z = 10.0


0.013% 1.40% 7.47% 9.29% 81.82%0.001 0.121 0.579 0.260 0.035 0.005 469.810.010 0.057 0.466 0.366 0.081 0.030 54.080.100 0.050 0.444 0.378 0.090 0.038 5.980.500 0.049 0.442 0.379 0.091 0.039 1.281.000 0.049 0.441 0.380 0.091 0.039 0.662.000 0.049 0.441 0.380 0.091 0.039 0.344.000 0.049 0.441 0.380 0.091 0.039 0.188.000 0.049 0.440 0.380 0.092 0.039 0.0930.000 0.048 0.437 0.381 0.093 0.041 0.03100.000 0.046 0.430 0.385 0.096 0.044 0.01500.000 0.039 0.402 0.397 0.107 0.055 0.001000.000 0.034 0.385 0.405 0.114 0.062 0.00


A = 0.15000 E-12 MAX Z = 10.0


0.013% 1.40% 7.47% 9.29% 81.82%0.001 0.121 0.579 0.260 0.035 0.005 437.200.010 0.057 0.466 0.366 0.081 0.030 49.800.100 0.050 0.444 0.378 0.090 0.038 5.460.500 0.049 0.442 0.379 0.091 0.039 1.161.000 0.049 0.441 0.380 0.091 0.039 0.602.000 0.049 0.441 0.380 0.091 0.039 0.314.000 0.049 0.441 0.380 0.091 0.039 0.168.000 0.049 0.440 0.380 0.092 0.039 0.0830.000 0.048 0.437 0.381 0.093 0.041 0.02100.000 0.046 0.430 0.385 0.096 0.044 0.01500.000 0.039 0.402 0.397 0.107 0.055 0.001000.000 0.034 0.385 0.405 0.114 0.062 0.00

A = 0.15000 E - 12 MAX Z=5.0


0.013% 1.40% 7.47% 9.29% 81.82%0.001 0.116 0.578 0.265 0.036 0.005 436.060.010 0.055 0.460 0.370 0.083 0.032 49.350.100 0.050 0.443 0.379 0.090 0.038 5.390.500 0.049 0.441 0.379 0.091 0.039 1.151.000 0.049 0.441 0.380 0.091 0.039 0.592.000 0.049 0.441 0.380 0.091 0.039 0.304.000 0.049 0.440 0.380 0.091 0.039 0.168.000 0.049 0.439 0.380 0.092 0.040 0.0830.000 0.048 0.434 0.383 0.094 0.042 0.02100.000 0.044 0.422 0.388 0.099 0.047 0.01500.000 0.035 0.387 0.404 0.113 0.061 0.001000.000 0.031 0.372 0.411 0.119 0.067 0.00


THE MEASURING OF ETHER-DRIFT VELOCITY AND

KINEMATIC ETHER VISCOSITY WITHIN OPTICAL

WAVES BAND

Yu.M. Galaev1

The Institute of Radiophysics and Electronics of NSA in Ukraine,12 Ac. Proskury St., Kharkov, 61085 Ukraine

Received November 15, 2002

The experimental hypothesis veri�cation of the ether existence in nature, i.e. the material medium, responsiblefor electromagnetic waves propagation has been performed. The optical measuring method of the ether movementvelocity and the ether kinematic viscosity has been proposed and realized. The results of systematic measurementsdo not contradict the original hypothesis statements and can be considered as experimental imagination con�rmationof the ether existence in nature, as the material medium.

The experimental hypothesis veri�cation of theether existence in nature, i.e. material medium, respon-sible for electromagnetic waves propagation has beenperformed earlier in the works [1-3], within millimeterradio waves band, by the phase method. The results ofthe experiment [1-3] do not contradict the original hy-pothesis statements, based on the ether model of V.A.Atsukovsky [4-6]. In the model [4-6] the ether is intro-duced by the material medium composed of separateparticles, that �lls in the world space, has the prop-erties of viscous and coercible gas, is the constructionmaterial for all material formations. The physical �eldsrepresent the ether various movement forms, i.e. theether is the material medium, responsible for electro-magnetic waves propagation. The experimental modelbasis [4-6] was, �rst of all, the positive results of theether drift search published by D.C. Miller in 1922-1926[7-9] and A.A. Michelson, F.G. Pease and F. Pearsonin 1929 [10].

The experiment [7-9] is performed within the elec-tromagnetic waves optical band, di�ered by carefulpreparation, veri�ed methods of the investigation con-ducting and statistically signi�cant measurement re-sults. The measured ether drift parameters mismatchedto the ether imaginations available at that time, as sta-tionary medium. Orbital component of the ether driftvelocity, stipulated by the Earth movement around theSun with the velocity 30 km/sec, was not detected.Miller obtained, that the ether drift velocity at theheight of 265 m above the sea level (Clevelend, USA)has the value about 3 km/sec, and at the height of1830 m (Mount Wilson observatory, USA) | about 10

1e-mail: [email protected]; Ph.: +38 (0572) 27-30-52

km/sec. The apex coordinates the Solar system move-ment were determined: direct ascension � � 17:5h ,declination � � +65� . Such movement is almost per-pendicular to an ecliptic plain (coordinates of the NorthPole ecliptic: � � 18h , � � +66� ). Miller showed, thatthe observed e�ects can be explained, if to accept, thatthe ether stream has a galactic (space) origin and thevelocity more than 200 km/sec. Almost perpendicu-larly directional orbital component of the velocity islost on this background. Miller referred the velocitydecrease of the ether drift from 200 km/sec up to 10km/sec to unknown reasons.

Some peculiarities of the experiment results [7-9]and [10], are explained by the ether viscosity in theworks [4-6]. In this case the boundary layer, in whichthe ether movement velocity (the ether drift) increas-es with the height growth above the Earth's surface, isformed at the relative movement of the solar Systemand the ether near the Earth's surface.

In the works [1-3] it is shown, that the results of sys-tematic experimental investigations within radio wavesband can be explained by the wave propagation phe-nomenon in the moving medium of a space origin witha vertical velocity gradient in this medium stream nearthe Earth's surface. The gradient layer availability canbe explained by this medium viscosity, i.e. the featureproper to material media, the media composed of sep-arate particles. The mean value of the measured maxi-mal gradients was equal to 8.6 m/sec � m. The velocitycomparison of the suspected ether drift, measured inthe experiments [1-3], [7-9] and [10], is performed in theworks [1-3]. The place distinctions of geographic lati-tudes and their heights above the sea level are taken

208 Yu.M. Galaev

into account in these experiments conducting at com-parison. It is obtained, that in the experiment [1-3] theether drift velocity is within 6124 : : :8490 m/sec, thataccording to the value order coincide with the data ofthe works [7-9] and [10], which are within 6000 : : :10000m/sec. The comparison result can be considered as mu-tual truthfulness con�rmation of the experiments [1-3],[7-9] and [10].

The positive results of three experiments [1-3], [7-9], [10] give the basis to consider the e�ects detectedin these experiments, as medium movement develop-ments, responsible for electromagnetic waves propaga-tion. Such medium was called as the ether [11] at thetimes of Maxwell, Michelson and earlier. The conclu-sion was made in the works [1-3], that the measurementresults within millimeter radio waves band can be con-sidered as the experimental hypothesis con�rmation ofthe material medium existence in nature such as theether. Further discussions of the experiment results[1-3] have shown the expediency of additional experi-mental analysis of the ether drift problem in an opticalwave band.

Experiments [7-9] and [10] are performed with opti-cal interferometers manufactured according to the cru-ciform Michelson's schema [12,13]. The work of suchinterferometer based on the light passing in a forwarddirection and returning it to the observing point alongthe same path. The Michelson's interferometer sensi-tivity was low to the original ether drift e�ects. Themeasured value D in such a device, i.e. visually ob-served bands o�set of an interference pattern expressedin terms of a visible bandwidth, is proportional to ve-locity ratio quadrate of the ether drift W to the lightvelocity c , the optical length of the light beam l andis inversely proportional to the wave length of electro-magnetic emission (light) � [12].

D = (l=�) (W=c)2 : (1)

We shall call the interval, which a beam passes in theinterferometer measuring part, as the optical length ofthe light beam. The research methods and experimentsin the investigations of the ether drift, in which themeasured value is proportional (W=c)2 was called asthe "methods and experiments of the second order".Accordingly the methods and experiments, in which themeasured value is proportional to the �rst ratio extentW=c are called as the methods and experiments of the�rst order. The ratio is W/c � 1 at the expectedvalue in the experiments of Michelson, Miller W � 30km/sec. The methods of the second order are ine�ectiveat this requirement. So at W � 30 km/sec the methodof the second order in 10000 (!) times succumbs onsensitivity to the method of the �rst order. Howeverat that time the methods of the �rst order, suitable forthe ether drift velocity measuring, were not known.

The expression (1) allows to estimate the di�culties,with which the explorers of the ether drift confronted

in the �rst attempts while observing the e�ects of thesecond order. So in the widely known �rst experimentof Michelson 1881 [12], at the suspected velocity valueof the ether drift W � 30 km/sec, with the interfer-ometer having parameters: � � 6 � 10�7 m; l � 2:4m, it was expected to observe the value D � 0:04 ofthe band. And it is in the requirements of considerableband shivering of an interference pattern. In the work[12] Michelson marked: "The band were very indistinctand they were di�cult for measuring in customary con-ditions, the device was so sensitive, that even the stepson the sidewalk in a hundred meters from the observa-tory caused the complete bands vanishing!". Later, in1887, Michelson, also in his world-known work [14], to-gether with E.V.Morly, once again marked the essentialde�ciencies of his �rst experiment as for the ether drift[12]: "In the �rst experiment one of the basic considereddi�culties consisted in the apparatus rotating withoutthe distorting depositing, the second | in its exclusivesensitivity to vibrations. The last was so great, thatit was impossible to see interference bands, except shortintervals at the business-time in the city, even at 2 a.m.At last, as it was marked earlier, the value, which shouldbe measured, i.e. the interference bands o�set becauseof something on the interval, smaller, than 1=20 of theinterval between them, is too small, to determine it,moreover at laying inaccuracies of the experiment".

In Miller's interferometer, for sensitivity increase,the optical path length in each of shoulders reached upto 64 meters [7-9]. It was gained due to applying ofmultiple re ection. The actual length of shoulders wasreduced up to 4 meters. In the experiment [10] theoptical length of the path reached 26 meters. In theexperiments [7-9] and [10] the interferometers laid onrafts, placed in tanks with quicksilver, that allowed toremove the in uence of exterior mechanical clutters.

The positive results of Miller's experiment by virtueof their general physical signi�cance attracted the physi-cists' great attention at that time. In the monographs[15] 150, devoted to the ether drift's problem and refer-ring to 1921-1930, are mentioned that almost everyonewere concentrated on the discussion of Miller's results.The possible in uencing of the di�cult considered ex-terior reasons (temperature, pressure, solar radiation,air streams etc.) on the optical cruciform interferom-eter, sensitive to them, which had considerable overalldimensions [16] in Miller's experiments was discussedmost widely in these works. Besides by virtue of me-thodical limitations being in the works [7-9] and [10],their authors did not manage to show experimentallycorrectly, that the movement, detected in their exper-iments, can be explained by the Earth relative move-ment and the medium of material origin, responsiblefor electromagnetic waves propagation [1-3]. Howeverthe most essential reason, which made Miller's con-temporaries consider his experiments erratic, was thatin numerous consequent works, for example, such as

The measuring of ether-drift velocity and kinematic ether viscosity within optical waves band 209

[17-20], Miller's results were not con�rmed. In theexperiments [17-20] so-called the \zero results" wereobtained, i.e. the ether drift was not detected.

Thus, taking into consideration the works de�cien-cies [7-9], [10] and a major number of experiments witha zero result available, it is possible to understand thephysicists' mistrust to the works [7-9], [10] at that time,the results of which pointed the necessity of the fun-damental physical concept variations. The analyticalreview of the most signi�cant experiments, performedwith the purpose of the ether drift search, is explainedin the works [1-3, 21].

In 1933 D.K. Miller, in his summary work [22], per-formed the comparative analysis of multiple unsuccess-ful attempts of his followers to detect the ether driftexperimentally. He paid attention that in all such at-tempts, except the experiment [10], optical interferom-eters were placed in hermetic metallic chambers. Theauthors of these experiments tried to guard the devicesfrom exposures with such chambers. In the experi-ment [10] it was placed into a fundamental building ofthe optical workshop at the Mount Wilson observato-ry for stabilizing the interferometer temperature sched-ule. The hermetic metallic chamber was not applied,and the ether drift was detected. Its velocity had thevalue W � 6000 m/sec. Miller made the conclusion:"Massive non-transparent shields available are undesir-able while exploring the problem of ether capturing. Theexperiment should be made in such a way that therewere no shields between free ether and light way in theinterferometer".

Later, new opportunities for conducting experi-ments on the ether drift discovery have appeared alsoafter the instruments occurrence based on completelydiverse ideas (resonators, masers, Messbauer's e�ectetc.). Such experiments were held [23-26]. And againthe massive metallic chamber usage was the commoninstrumental error of these experiments. In the works[23,24,26] there were the metallic resonators, in thework [25] | a lead chamber, because it was neces-sary to use gamma radiation. The authors of theseworks, perhaps, didn't pay attention to Miller's conclu-sions of 1933 about the bulk shields inapplicability inthe ether drift experiments. The phenomena physicalinterpretation of the essential ether drift velocity re-duction at metallic shields available was given by V.A.Atsukovsky for the �rst time, having explained majorether-dynamical metal resistance of a Fermi's surfaceavailable in them [6].

The purpose of the work is the experimental hy-pothesis test of the ether existence in nature within anoptical electromagnetic waves band | material medi-um, responsible for electromagnetic waves propagation.It is necessary to solve the following problems for reach-ing this purpose. To take into account the de�cienciesthat occurred in the experiments earlier conducted. Toelaborate and apply an optical measuring method and

the metering device, which does not iterate the Michel-son's schema, but being its analog in the sense of resultinterpretation. (Michelson's interferometer of the sec-ond order is a bit sensitive to the ether streams and toosensitive to exposures.) To execute systematic measure-ments in the epoch of the year corresponding to theepoch of the experiments implementation [1-3], [7-9],[10]. (The term "epoch" is borrowed from astronomy,in which the observation of di�erent years performed inthe months of the same name, refer to the observationsof one epoch.) The results of systematic measurementsshould be compared to the results of the previous ex-periments. The positive result of the experiment canbe considered as experimental hypothesis con�rmationof the ether existence in nature as material medium.

Measuring method. The ether model, proposedin the works [4-6], was accepted at making the experi-ment. The following e�ects should be observed experi-mentally within the original hypothesis:

The anisotropy e�ect | the velocity of electromag-netic waves propagation depends on radiation direction,that is stipulated by the relative movement of the so-lar System and the ether - the medium, responsible forelectromagnetic waves propagation.

The height e�ect| the velocity of wave propagationdepends on the height above the Earth's surface, thatis stipulated by the Earth's surface interaction with theviscous ether stream - material medium, responsible forelectromagnetic waves propagation.

The space e�ect | the velocity of wave propaga-tion changes its value with a period per one stellar day,that is stipulated by a space (galactic) origin of theether drift | the medium, responsible for electromag-netic waves propagation. Thus the height (astronomi-cal coordinate) of the Solar system movement apex willchange its value with the period per one stellar dayas well as for any star owing to the Earth's daily rotat-ing. Therefore the velocity horizontal component of theether drift and, hence, the velocity of electromagneticwave propagation along the Earth's surface will changethe values with the same period.

The hydroaerodynamic e�ect | the velocity of elec-tromagnetic waves propagation depends on movementparameters of viscous gas-like ether in directing systems(for example, in tubes), that is stipulated by solids in-teraction with the ether stream|material medium, re-sponsible for electromagnetic waves propagation. (As itis known, the law of uids and gases motions and theirinteraction with solids is learnt by hydroaerodynamics.This e�ect, apparently, should be called as the ether-dynamics e�ect with reference to the ether dynamics.It can be seen, that "the height e�ect" is referred tothe etherdynamic e�ect class. However in the work, byvirtue of methodical reception distinction used for theirdiscovery, the e�ects are indicated as separate).

According to the investigation purpose, the measur-ing method should be sensitive to these e�ects.

210 Yu.M. Galaev

The following model statements are used at mea-suring method development [4-6]: the ether is a ma-terial medium, responsible for electromagnetic wavespropagation; the ether has properties of viscous gas;the metals have major etherdynamic resistance. Theimagination of the hydroaerodynamic (etherdynamic)e�ect existence is accepted as the initial position. Themethod of the �rst order based on known regularitiesof viscous gas movement in tubes [27-28] has been pro-posed and realized within the optical electromagneticwaves band in the work for measuring of the ether driftvelocity and ether kinematic viscosity.

The method essence is in the following. Let's placea tube part into a gas stream in such a way, that thedirect tube axis will be perpendicular to the streamvelocity vector. In this case both opened tube ends inrelation to an exterior gas stream are in identical condi-tions. The gas pressure drop does not occur on the tubepart, and the gas inside a tube will be immobile. Thenwe shall turn a tube in such a way, that the velocity vec-tor of a gas stream will be directed along the tube axis.In this case the gas speedy stream will create a pressuredrop on the tube ends, under action of which there isa gas stream in a tube soon. The stabilization time ofa gas stream in a tube and this stream velocity are de-termined by the values of gas kinematic viscosity, thegeometrical tube sizes and the velocity of an exteriorgas stream [27-28]. Let's mark, that the developmentof constant gas stream in a tube lasts a terminatinginterval of time. The ether is a gas-like material medi-um, responsible for electromagnetic waves propagationaccording to the accepted hypothesis. It means, thatthe electromagnetic wave velocity regarding to the ob-server is the sum of wave velocity vectors relative to theether and the ether velocity with regard to the observer.In this case, if an optical interferometer is created, inwhich a beam drives inside a metallic tube, and anotheroutside of a tube (in the ether exterior stream) and toturn the interferometer in the ether drift stream, it canbe expected, that in such interferometer, during a sta-bilization time of the ether stream in a tube, the bandso�set of the interference pattern regarding to the orig-inal position of these bands on the interferometer scaleshould be observed. Thus the value of bands o�set willbe proportional to the ether exterior stream velocity,and the stabilization time | the bands return time tothe original position, will be de�ned by the ether kine-matic viscosity value. Hence, the proposed measuringmethod enables to meter the ether drift velocity valuesand the ether kinematic viscosity. The proposed mea-suring method is a method of the �rst order, as it is notrequired to revert a light beam to the initial point (as,for example, in Michelson's interferometer).

Let's calculate the interferometer parameters. Forthe stream analysis of the gas-like ether we shall usethe mathematical hydrodynamics apparatus, which isadvanced in the works [27-28] at the problem solving,

connected with the stream of viscous incompressible u-id. The use of such solutions for gas stream analysis istrue, if the following requirement is performed

0:5Ma2 << 1; (2)

where Ma = wpac�1s is a Mach's number; wpa is anaverage gas stream velocity on a tube section; cs is thegas sound velocity. At the requirement implementation(2), it is possible to neglect the gas pressure e�ects andconsider the gas stream as the stream of incompressible uid. On data of the experimental works [1-3], [7-9] and[10], the ether drift velocity W near the Earth's sur-face does not exceed the value W � 104 m/sec. In thework [6] the sound velocity in the ether is estimated bythe value cs � 1021 m/sec, that essentially exceeds thelight velocity. Even if to consider, that cs = c , we shallreceive, that Ma � 3:3 � 10�5 . Hence, the requirement(2) is performed, the stream of a gas-like ether can beconsidered as a stream of viscous incompressible uidand the use of the hydrodynamics corresponding math-ematical apparatus is true for ether stream analysis.

Laminar and turbulent uid streams are distin-guished in hydrodynamics. The laminar uid streamexists, if the Reynolds number Re , drawn up for astream, does not exceed some extreme value Rec [27-28]

Re < Rec: (3)

The Reynolds number for a round cylindrical tubeis de�ned by the following expression

Re = 2apwpa��1; (4)

where ap is the interior tube radius; v = ��1 is kine-matic uid viscosity; � is the dynamic viscosity; � isthe uid density. Depending on the exterior stream na-ture and the requirements of uid in ux into a tube,the values Rec are within Rec � 2:3 � 103 : : :104 . AtRe < 2:3 � 103 the uid stream in a tube exists only aslaminar and does not depend on an extent of an exteriorstream turbulence. The following features are peculiarfor a steady laminar uid stream in a round cylindricaltube. The particle movement pathways are rectilinear.The maximal uid stream velocity wpmax takes placealong the tube axis and is equal to

wpmax = 0:25�pa2p��1l�1p ; (5)

where �p is the pressure drop on a tube part with thelength lp ;

�p = 0; 25 plpa�1p �w2

pa; (6)

p is the coe�cient of a round tube resistance, which isequal p = 64Re�1 at a laminar regime of uid stream.The maximal stream velocity wpmax is twice more thanmean uid velocity

wpmax = 2wpa: (7)


Figure 1: A tube in a gas stream

The stream velocity distribution on a tube sectionis called as Puazeyl's parabola and looks like

wp (r) = wpmax

�1� r2a�2p

�; (8)

where r is the coordinate along the tube radius.The laminar stream transferring into a turbulent

one takes place not uently, but by jumps. At transfer-ring through the extreme value of a Reynold's numberthe tube resistance coe�cient increases by jump, andthen slowly reduces. The following features are peculiarfor a steady stream of viscous liquid in a round cylindri-cal tube of turbulent stream. The pathways of particlemovement have scattered nature. The resistance coe�-cient of a round tube is equal p = 0:3164Re�0:25. Thevelocity distribution on a tube section is almost uni-form with their sharp reduction up to zero point in athin layer near the wall. The maximal velocity increaseabove the mean order value is about 10-20 % [27-28]

wpmax � (1:1 : : :1:2)wpa: (9)

It will be shown below, that in the experiment re-quirements, as a rule, Re > Rec , therefore in the workwe shall be restricted by the estimations, performed forthe ether turbulent stream.

Let's consider the method operating principle. Inthe Fig. 1 the part of a cylindrical round metallic tubewith the length lp , which is in the ether stream (etherdrift), is shown

The ether stream is shown in the �gure as slant-ing thin lines with arrows, that indicate the directionof its movement. The tube longitudinal axis is locat-ed horizontally and along with the ether drift velocityvector is in a vertical plain, which represents the �gureplain. The tube walls have major ether-dynamic resis-tance and the ether stream acting from the tube sur-face side area, the ether inside a tube does not move.The ether velocity stream stipulated by the horizontalvelocity component of the ether drift Wh , creates theether stream in a tube, which goes with the mean ve-locity wpa . It can be spoken, that the metallic tube isthe routing system for the ether stream. Let's turn atube in a horizontal plain in such a way, that its lon-gitudinal axis will take up a position perpendicular to

the plain of the Fig. 1 or, that is similar | perpen-dicular to the velocity vector of the ether drift. In thisposition both opened ends of a tube will be in identicalconditions regarding to the ether stream, the pressuredi�erential �p does not occur and according to (5) theether stream velocity in a tube is equal to a zero point.At the moment t0 we shall turn a tube into the initialposition. The horizontal component of the ether driftvelocity Wh will create a pressure drop �p on the tubeends, under operation of which the ether stream will bedeveloped in a tube. In the work [28] the problem aboutsetting into motion of viscous incompressible uid beingin a round cylindrical tube under operating of the sud-denly appended constant pressure drop �p is solved.Let's reduce the formula of the velocity distribution of uid stream in a tube

wp (r; t) = wpmax

�1� r2

a2p�

� 81Xk=1

J0� kra�1p

� 3kJ1 ( k)

exp

��

2kt

a2p

�#; (10)

where t is the time; k is the equation roots J0 ( k) =0; J0; J1 are Bessel's functions of the zero and �rstorders. The �rst two summands in square brackets ex-press steady (at t ! 1) laminar stream of uid andcorrespond the mentioned above \Puazeyl's parabola"(8). So at a turbulent uid stream, according to (9),the velocity distribution on a tube section is almost uni-form, we shall consider, that the uid stream velocityis equal wpa on the whole tube section (the value pof the round tube at a turbulent uid stream should beused at the value calculation wpa ) except the thin near-wall layer. In this case the expression (10) at r = 0 willbe like

wp (t) � wpa

"1� 8

1Xk=1

�3k J�11 ( k) �

� exp �� 2ka�2p t��: (11)

The expression (11) describes the process of a uidstream de�ning in a round tube. It follows from (11),that at t ! 1 the value is wp (t) ! wpa . Both partsof the expression (11) should be divided into the valueof constant uid stream velocity in a round tube wpa .In this case the time variation of uid stream dimen-sionless velocity wp (t)/wpa will be like, that is shownin a Fig. 2.

In the �gure the values of dimensionless velocitywp (t)/wpa are given on an ordinates axis, the valuesof time are given on the abscissa axis. As it is shownabove, the requirement (2) is performed and the etherstream can be described by the laws of thick liquid mo-tions, then we shall speak about the ether stream fur-ther, instead of uid. In the Fig. 2 we'll allocate the

212 Yu.M. Galaev

Figure 2: Variation in time of uid movement velocity in atube

interval of time t0 : : : td , during which the ether streamvelocity in a tube changes from 0 up to 0.95 wpa . Weshall call the ether stream regime on this time inter-val as the dynamic one. We shall call the ether streamregime at t > td as the steady stream regime.

Let's skip a light beam along the tube axis. It canbe written down, that the phase of a light wave on a cutwith the length lp will vary on value j, which is equal.

' = 2�f lpV�1; (12)

where f is the electromagnetic wave frequency; V isthe light velocity in a tube. According to the originalhypothesis the ether is a medium, responsible for elec-tromagnetic waves propagation. This implies, that if ina tube with the length lp there is the ether stream, thevelocity of which changes in time, so the phase of a lightwave measured on the tube output, should change intime according to variation in time of the ether streamvelocity wp (t). Then the expression (12) will be like

' (t) = 2�f lp [c� wp (t)]�1 ; (13)

where c is the light velocity in a �xed ether, in vacuum.In the expression (13) the sign "+" is used, when thedirection of the light propagation coincides with theether stream direction in a tube, and the sign "-" isused, when these directions are opposite.

In the work the optical interferometer is applied formeasuring value ' (t) . Rozhdestvensky's interferome-ter schema is taken [29] as the basis, which is supple-mented in such a way, that the light beam drove alongthe empty metallic tube axis in one of the shoulders.The interferometer schema and its basic clusters areshown in the Fig. 3.

1 | illuminator; 2 | a metallic tube part; 3 |eyefragment with a scale; P1 , P2 | at parallel semi-transparent laminas; M1 , M2 | mirrors are shown onthe schema. The beam course is shown with thick linesand arrows. The light beam in a tube pass along theaxis and is indicated with a broken line in the �gure.The tube length is lp � P1M1 . The clusters P1 , M1

Figure 3: The schema of an optical interferometer

and P2 , M2 are mounted two by two parallelly, M1 ,M2 are mounted opposite each other on a small angle.The angles i1 , i2 are the angles between normals tothe mirror plains M1 , M2 and the beams dropping onthem. The intervals are P1M1 = M2P2 = l1 , M1P2 =P1M2 � lp . In a classical case if the ether drift in uenceisn't considered, the Rozhdestvensky's interferometeroperating is reduced to the following. The light beamwith the wave length � is divided P1 into two beams,which after re ection from M1 and M2 and passing P2are parallel with a phase di�erence [29]

� = 4� l1��1 (cos i1 � cos i2) : (14)

The angles i1 , i2 are established at the interferom-eter adjustment so that the interference pattern shouldbe observed. (The adjustment clusters are not shownon the schema symbolically). In a tuned interferometerthe value is � = const . In the right part of the Fig. 3the family of arrows means the stream direction of theether drift horizontal component velocity. This streamvelocity is equal to Wh . If to arrange the interferom-eter clusters on a horizontal rotated background, suchinstrument can be turned in the ether stream. The ro-tation axis is perpendicular to the �gure plains and isindicated as Ai .

In the interferometer (Fig. 3) the band position ofan interference pattern regarding to the eyefragmentscale 3 is de�ned by the phase di�erence of the lightbeams, which are distributed on the paths P1M2P2 andP1M1P2 . In the Fig. 3 the ether stream is directedtowards the light propagation direction along the beamsP1M2 , M1P2 . In this case, according to (13), we shallwrite down expression for the phase di�erence �' (t)between the beams P1M2P2 and P1M1P2 .

�' (t) = 2�f

��P1M2

c� wp (t)+M2P2c

��

��P1M1

c+

M1P2c�Wh

��+ �; (15)

where � is constant, the value of which is de�ned bythe expression (14). Let's simplify the expression (15).


For this purpose we shall introduce the identi�cationsaccepted earlier. Allowing, that the beam phase dif-ference M2P2 and P1M1 does not depend on the in-terferometer orientation regarding to the ether streamdirection and is equal to zero point, the expression forthe value �' (t) will be like

�' (t) = 2�f lp

�1

c�wp (t)� 1

c�Wh

�+ �: (16)

The �rst member of the expression (16) describesthe beam phase variation P1M2 depending on the etherstream velocity in a tube wp (t). The second memberis the beam phase variation M1P2 depending on theether exterior stream velocity Wh . Let's reduce the ex-pression in square brackets to a communal denomina-tor and, allowing, that c2 �Whwp (t)� cwp (t)� cWh ,fc�1 = ��1 we shall receive

�' (t) � 2� lp�

�wp (t)�Wh

c

�+ �: (17)

It follows from the expression (17), that the di�er-ence in the phase �' (t) between beams P1M2P2 andP1M1P2 is proportional to a di�erential of the etherstream velocity in a tube wp (t) and the ether exteriorstream Wh .

Let's consider the interferometer operating in itssteady regime, at t!1 . According to the expression(11) and Fig. 2 wp (t)t!1 ! wpa it can be suspect-ed, that owing to the small value of the ether dynamicviscosity (celestial bodies move in the ether) the ethersteady stream velocity in a tube regarding to the smalllength will not di�er essentially from the ether exteriorstream velocity and it is possible to write down, thatwp (t)t!1 = wpa � Wh . (The correctness of this sup-position in the work is determined experimentally andshown below.) In this case in the expression (17) thefraction numerator in square brackets is equal to zeropoint, and this expression will be

�' (t)t!1 � �: (18)

Hence, in the steady regime the interferometer op-erating with a metallic tube does not di�er from theRozhdestvensky's interferometer operating. In both in-terferometers the bands position of an interference pat-tern will be de�ned by the original phase di�erence � .The interferometer, with a metallic tube, in the steadyoperating regime is not sensitive to the ether drift ve-locity and can not detect the availability or absence ofthe ether drift.

Let's consider a dynamic operating regime of theinterferometer. Let's unroll the interferometer (see Fig.3) in the horizontal plain at 180� . As the direction ofthe light propagation has varied in relation to the etherdrift stream to the opposite one, the expression (17)will be like

�' (t) � 2� lp�

�Wh �wp (t)

c

�+ �: (19)

According to the expression (11) and the Fig. 2, theinequality wp (t) < Wh takes place at the time intervalt0 : : : td . Hence, in a dynamic regime the interferom-eter with a metallic tube is sensitive to the velocitydi�erential of the ether exterior stream velocities Wh

and the ether stream inside a tube wp (t) . We shalldiscover the bands o�set value of the interference pat-tern regarding to their position in the interferometersteady work regime as follows. Let's take a di�erentialof the expressions (19), (18) and divide both parts ofthe found expression into 2� , we shall receive

�' (t) ��' (t)t!12�

=lp�

�Wh �wp (t)

c

�: (20)

The expression left-hand part (20) is equal to therequired interference pattern o�set, which is expressedby the number of electromagnetic wave periods. Withreference to the visually observed interference patternthe expression (20) describes the value variation in timeof visible bands o�set of this pattern regarding to theiroriginal position | D (t) . The visible bandwidth valueof an interference pattern can be the o�set measure-ment unit. Taking into consideration, that the etherstream in a tube can have the direction opposite to theselected on the Fig. 3, generally it is possible to receive

D (t) = � lp�

�Wh �wp (t)

c

�: (21)

In the expression (21) the sign "+" is used, whenthe light propagation direction coincides with the etherstream direction in the interferometer dynamic regimein a tube, and the sign "-" is used, when these directionsare opposite. According to the expression (11) and theFig. 2 at an instant t0 = 0 the ether stream velocity ina tube is wp (t0) = 0. Then from (21) we shall receive,that at the instant t0 the bands o�set of an interferencepattern accepts the maximal value equal to

D (t0) = � lp�� Wh

c; (22)

and in the steady regime, when the ether velocity in atube is equal to wp (t)t!1 � Wh , the bands o�set re-garding to their original position is equal 0. The depen-dence view D (t) can be obtained with the dependencewp (t)/wpa , which is shown in the Fig. 2. Really, let'sdivide (21) into (22), we shall receive

D (t)

D (t0)= 1� wp (t)

Wh: (23)

Allowing the supposition made above, that wp (t)t!1= wpa � Wh the expression (23) can be written downas D (t)/D (t0) � 1�wp (t)/wpa . The dependence viewobtained in such a way, is shown in the Fig. 4

In the expression (22) the measured value D is pro-portional to the �rst extent of the ether drift velocity ra-tio to the light velocity, that characterizes the reviewed

214 Yu.M. Galaev

Figure 4: Variation in time of interference pattern bandso�set in a dynamic interferometer operating regime

method as the �rst order method. It follows from theexpression (22) and the Fig. 4, that if at the moment oftime t0 to measure the bands o�set value D regardingto their original position on the interferometer eyefrag-ment scale, it is possible to determine the ether driftvelocity horizontal component Wh which is equal to

Wh = �D (t0) c�l�1p ; (24)

The direction of the interference pattern bands o�-set, regarding to their original position, will be de�nedby the ether exterior stream direction.

The data of the interferometer tube sizes are nec-essary for the proposed measuring method realization.The expression for the tube interior radius calcula-tion ap can be obtained as follows. Let's divide bothparts of the expression (11) on wpa and, allowing, thatat the moment of time td (see the Fig. 2) the ratiowp (t)/wpa = 0:95, we shall write down as

1� 81Xk=1

�3k J�11 ( k) exp�� 2ka�2p td

�=

= 0:95: (25)

If to be con�ned by the estimation accuracy noworse than 7 %, so the series in the expression (25) canbe exchanged by its �rst member. Let's substitute inthe (25) the numerical values k and J1 ( k) (for theinformation we shall give these values: 1 = 2:4048;J1 ( 1) = 0:5191), we shall receive

ap � 1:37 (td�)1=2 : (26)

The expression (26) allows to calculate such the in-terferometer design parameter as the tube radius ap .At calculation, the value td is selected coming from thetime, which is required for implementation of visual (ortool) readout of bands o�set value D . The data ofthe ether kinematic viscosity value v will be reviewed

below. The tube length lp can be found with the ex-pression (24), of which we shall receive

lp � Dmin (t0)�cW�1hmin; (27)

where Dmin (t0) is bands o�set minimum value of aninterference pattern, which can be digitized with theselected eyefragment and scale; Whmin is the minimumvalue of the ether drift horizontal component velocity,which should be measured by the interferometer (theinterferometer sensitiveness).

The ether kinematic viscosity. The data of theether kinematic viscosity value v are necessary for themeasuring method realization. Let's estimate the valuev , relying on the following. In the work [5] the photonformation mechanism is represented, as the oscillatingresult of excited atom electronic shell in the ether andthe Karman's vortex track as hydromechanical photonmodel is proposed. In other words the photon forma-tion is stipulated by the ether stream turbulent regimeof the excited atom streamlining by the ether, oscillat-ing in the ether. The turbulent pulsation propagationin the ether is perceived by the observer as the lightemission. In the work [28] it is shown, that the exis-tence of pulsation movement is possible in uid volume,if the Reynold's number is not lower than some extremevalue equal to

Recr = wd��1; (28)

where w is uid movement velocity; d is the charac-teristic size of a streamlined body. In the work [28] itis obtained, that Recr � 425. With reference to ourproblem the values w , d , v are accordingly: the ethermovement velocity, atom diameter, the ether kinematicviscosity. From the expression (28) we shall �nd

� � wdRe�1cr : (29)

We shall call the obtained ether kinematic viscosityvalue as the calculated ether kinematic viscosity valuevc . Let's calculate the value vc . As the ether streamvelocity w we shall accept the o�set velocity of elec-tronic atom shells in the immobile ether at a photonemission. Let's consider, that this velocity does not ex-ceed the light velocity w � c . The diameter of atoms,as it is known, has the value order d � 10�10 m. Inthis case with the (29) we shall receive

�c � 7:06 � 10�5 m2sec�1: (30)

The performed estimation has shown, that the etherkinematic viscosity calculated value corresponds tothe work imaginations [6] about the ether as gas-likemedium with real gas properties. So, the kinemat-ic viscosity values of twelve gases, spread in nature,are within 7 � 10�6 m2sec�1 (carbon dioxide) up to1:06 � 10�4 m2sec�1 (helium).


Figure 5: The interferometer structure

Optical interferometer. The calculated etherkinematic viscosity value allows to calculate the inter-ferometer parameters. With the expression (26) weshall determine the tube radius. If the value td is sup-posed to be equal 1 second, we shall receive, that atthe interferometer creation it is necessary to apply thetube with the interior radius ap � 0:05 m. We shalldetermine the tube length lp with the expression (27).If to suppose the values Dmin = 0:05, Whmin = 20m/sec and apply the light source with the wave length� = 6:5 � 10�7 m, so the required tube length is equalto lp � 0:49 m.

The optical interferometer was manufactured forconducting measurements. Schematic �gure of the de-vice (the top view) is shown in the Fig. 5.

In the Fig. 5 the identi�cations of the basic clustersare kept, which were introduced at viewing the inter-ferometer schema (Fig. 3). 4,5 | the interferometeradjustment clusters; 6,7 | racks for �xing at-parallelsemi-transmitting laminas and mirrors; 8 | interfer-ometer frame; 9 | power supply accumulators of theilluminator; 10 | the illuminator switch; 11 | the eye-fragment �xing cluster; 12 | heat-insulating housingare shown additionally. The frame 8 is manufacturedof a steel pro�le with � | like section. The wall thick-ness is 0.007 m. The pro�le height is 0.02 m. The framelength is 0.7 m, the width is 0.1 m. The interferometerclusters are �xed on a at frame surface. The racks 6,7 are manufactured of rectangular copper tubes withinterior section 0.01 m � 0.023 m. The light beamspass inside these tubes. The interval between beams isP1M2 and M1P2 it is equal 0.12 m. On racks, in thepoints P1 , P2 the at parallel semi-transmitting lam-inas, in the points M1 , M2 | mirrors are installed.(In the manufactured interferometer the at parallelglasses with the thickness 0.007 m were used as semi-transparent laminas). The laminas, mirrors and clus-ters of their �xing in the Fig. 5 are not shown symboli-cally. Each of the clusters 4,5 allows to change the racksposition in two orthogonal related plains. The tube 2is steel with the interior radius ap = 0:0105 m. The

tube length is lp = 0:48 m. The clusters of the tube�xing on 5 are not shown symbolically. The semicon-ductor laser with the wave length � � 6:5 � 10�7 m wasapplied as the illuminator. The optical paths in theinterferometer are located in a horizontal plain. Theinterferometer was located on a rotated material table,which was manufactured of an organic glass with thethickness 0.02 m. The heat-insulating gasket was putbetween the frame and material table . The interfer-ometer was closed by a common housing of six layers ofa soft heat-insulating material. The thickness of suchcoating was about 0.025 m. In the Fig. 5 the housingperimeter is shown. The housing background was thebox of rectangular section with the interior sizes: widthbc = 0:22 m, height hc = 0:11 m, length lc = 0:8 m.The box was manufactured of a cardboard with thethickness 0.007 m. In the box the face wall on theeyefragment part was absent. This opening was closedwith a common soft housing. The interferometer ro-tating was ensured with the end thrust bearing of thediameter 0.075 m. The bearing box is located betweenthe material table and support. The support is provid-ed with the units for the interferometer installation ina horizontal position.

The interferometer test. In the manufacturedinterferometer the minimumbands o�set of an interfer-ence pattern, which could be visually digitized, meantDmin = 0:05.

The device sti�ness was tested by two methods. Ac-cording to the �rst method the instrument frame wasmounted on a horizontal surface. The interferometer forone edge of a frame was hoisted in such a way, that theframe lean angles to the surface plain reached � 20� .In this position the interference patterns o�set frame,stipulated by elastic deformations of the instrument,did not exceed 0.3 bands (D = 0:3). According to thesecond method the instrument sti�ness was tested in aworking position. The frame lean angles up to 10� werecreated by the material table tilt. In this case the bandsnoticeable drift was not observed. The stability of aninterference pattern to impulsive loads was tested. Thelight shocks on the interferometer frame, material ta-ble and support caused short-lived interference patternwince at the moments of such strikes. Thus the inter-ference pattern was not destroyed. The bands saved anoriginal position after termination of impulsive loads.

The second stage of tests was performed on the ter-rain selected for experimental investigations. In windyweather the interference pattern was stable. The ob-server moving in an immediate proximity from theinterferometer installation site, the movement of thepedestrians and cars in 20 meters from the instrumentinstallation site did not cause the noticeable o�set orbands shivering. The short-lived bands shivering at carsmovement was marked on one of two selected points,which was in seven meters from a ground road. Thusthe interference pattern was observed, and the bands

216 Yu.M. Galaev

did not change the position. (The transport movementin this terrain is insigni�cant | on the average 3-4automobiles per a day.)

The interferometer heat tests were held in summer.The device was mounted on the open site. The variousdevice orientation on an azimuth was set in cloudlessweather conditions. In a �xed position the instrumentwas heated by solar radiation. In these conditions with-in 30 minutes the bands o�set did not exceed the valueD = 0:35 (� 1/100 bands for a minute). In cloudyweather and at night the interference pattern saved aninvariable position within 2-3 hours.

The measuring method sensitiveness to the etherdrift required e�ects was tested at the test �nal stage.The method of interferometer application was the fol-lowing. The instrument was mounted in a horizontalposition in such a way, that its direct axis coincidedwith a meridian line, and the illuminator was turned tothe north. In such initial position, in the interferome-ter steady work, the observer registered the bands orig-inal position of an interference pattern regarding to theeyefragment scale. The value D = 0 was given to thebands original position. Then the observer changed theposition | took a seat at the illuminator. The inter-ferometer turned in 180� . The rotational displacementwas performed within three seconds. At rotational dis-placement, as it was reviewed above, the ether stream ina tube was interrupted. The interferometer transferredinto a dynamic operating regime, which is described bythe expression (11). In this interferometer position themaximal value of bands o�set, the bands release timeto their original position was registered. The interfer-ometer transferred into a steady regime, and turnedinto the initial position. At this stage of tests it wasestablished, that after the dynamic regime terminationthe bands noticeable o�set of an interference patternregarding to their original position was not observed,i.e. bands o�set value D (t)t!1 � 0. According to theexpression (21) it means, that the ether stream velocityalong the tube axis at t ! 1 di�ered a bit from theether exterior stream velocity, that the value D was be-hind the interferometer threshold. It can be explainedby small resistance of the interferometer tube to theether stream movement inside this tube. Let's considerin this case, that

wp (t)t!1 = wpa � Wh: (31)

This experimental result was used above at the pro-portion deduction (18).

At procedure implementation, described above, itwas marked, that at the whole time course of value Dvariations corresponded to variations, which are shownin the Fig. 4 that did not contradict the original imag-inations about the interferometer work. The measuredduration of a dynamic regime meant td � 10 : : :13sec .The values ambiguity td is stipulated, �rst of all, by the

Figure 6: Observed variation in time of the interferencepattern bands o�set in the interferometer dynamic operat-ing regime

di�culties, connected with small values visual readoutof the value D , slowly changing, at the dynamic regimeend, i.e. at t! td . In the Fig. 6 the dependence viewD (t), created on the data visual observations, is shown.

However, as it can be seen in the Fig. 6, on theoriginal site by the extent about 1 second the depen-dence time course D (t) di�ered from an expected timecourse qualitatively. After the device rotation in 180� ,at the moment of time t0 , the bands still occupiedthe initial position, i.e. D (t0) = 0 instead of antic-ipated, according to (22) and the Fig. 4, the valueD (t0) = max . Since the moment t0 , the value Dwithin the time tm � 1sec reached the maximal value.There were suppositions of certain mechanical stressesin uencing at the interferometer braking after its rota-tion in 180� or other reasons, connected, for example,with air movement inside a heat-insulating housing. Inthis connection di�erent methods of the interferome-ter starting into movement and its braking were test-ed. The tests have shown, that the observed featureof the interferometer work could not be explained bythe suppositions made. The systematic round-the-clocktests have shown the following. The daily variations ofthe value D corresponded the measured ones in theexperiment [1-3] to the ether drift velocity variationswithin a day. (In the experiment [1-3] round-the-clockmeasurements were carried out continuously during 13months, since August 1998 till August 1999. The partof this experiment results is published in the works [1-3]. The measurement results within radio waves bandhave shown, that there is a rather small value of theether drift horizontal component velocity during thepart of a day. The same e�ects were marked at theoptical interferometer test in the work. The experi-ence has shown, that at a separate day, on such periodsof time at the interferometer rotation on 180� the no-


ticeable bands o�set of an interference pattern was notobserved. Hence, the detected features in dependenceD (t) (Fig. 6) could not be caused by the interferome-ter mechanical strains or air movements inside the in-terferometer heat-insulating housing, and are stipulat-ed by the exterior reasons. Such time periods, duringwhich D (tm) � 0 were used for improvement ways ofthe interferometer starting in rotation and its stopping.These ways were used then as standard procedures atsystematic measurement conducting.

Analysis of the interferometer test results.The detected regularity in the observed bands o�sethas required its physical interpretation. The possiblein uencing analysis of the interferometer structural el-ements on the ether streams has shown, that the ob-served dependence features D (t) can be qualitativelyand quantitatively described within the following sup-position. Let allow, that an exterior heat-insulatingdielectric housing of the interferometer (the point 12 inthe Fig. 5) forms the additional directing system for theether stream drift, besides a metallic tube. In this casethe exterior in relation to a metallic tube of the etherstream is the ether movement in a dielectric housing.If to consider the interferometer housing as the routingsystem, it is necessary to consider, that, since the mo-ment t0 in it, as well as in a metallic tube, the dynamicprocess of the ether stream de�ning will be developed.It gives the basis to write down the expression (21) asfollows

D (t) = � lp�

�Wc (t)� wp (t)

c

�; (32)

where Wc (t) is the variation of the ether stream ve-locity in time in the interferometer housing; wp (t) isthe variation of the ether stream velocity in time in ametallic tube.

The housing basis was a cardboard box of rectangu-lar section. Let's consider a problem about setting theether into motion, resting in a rectangular tube. Forthis purpose let's use the comparative method, spreadin hydrodynamics, of uid stream in a tube of a com-pound pro�le with uid stream in the tube of roundsection, "equivalent" on resistance, at which so-called"hydraulic" radius ah equal to an area ratio of a tubenormal section Gp to the section perimeter Np is ac-cepted [27] for this radius

ah = GpN�1p : (33)

Such a way enables to use the mathematical appa-ratus developed at stream analysis in round tubes. Asbefore we shall be limited to estimations, performed forthe ether turbulent stream. In this case the dependenceWc (t) can be calculated with the expression similar tothe expression (11) in which as the round tube radius

ap we shall use the "hydraulic" radius of a rectangulartube ah

Wc (t) � wpac

"1� 8

1Xk=1

�3k J�11 ( k) �

�exp �� 2ka�2h t��; (34)

where wpac is a mean velocity of the ether steady tur-bulent stream in the interferometer dielectric housing.As before, at considering the expression (17), and tak-ing into account the interferometer test results (31), it ispossible to consider, that the value wpac does not di�eressentially from the ether exterior stream velocity Wh

and it is possible to write down

Wc (t)t!1 = wpac � Wh: (35)

Let's calculate the value ah . Above, the housing in-terior overall dimensions were given at the interferom-eter structure description: width bc = 0:22 m, heighthc = 0:11 m. Then, having determined the values Gp

and Np , with the (33) we shall receive ah = 0:0367 m.From the expression (26) it is possible to see, that

the duration of the interferometer dynamic regime tdwill be de�ned by the tube of larger radius. As ah > ap ,the value td will be de�ned by the value of "hydraulic"radius of the interferometer housing ah

td � 0:53a2h��1: (36)

From the expression (36) it follows, that, having themeasured values td , it is possible to determine the etherkinematic viscosity value

� � 0:53a2ht�1d : (37)

The kinematic viscosity value, determined in sucha way, we shall call as the ether kinematic viscositymeasured value vc . Let's substitute into (37) the valuesah = 0:0367 m and the measured value td = (10 : : :13)sec, we shall receive

�e � (5:5 : : :7:1) � 10�5 m2sec�1: (38)

The kinematic viscosity mean value vea , calculatedas the function mean value v = f (td) within (10 : : :13)sec is equal to

�ea = 6:24 � 10�5 m2sec�1: (39)

Comparing (30), (38) and (39) we shall mark, thaton the value order the ether kinematic viscosity values,calculated and measured, coincide vc � ve � vea .

The opportunity of the problem solution about theether viscosity measuring is of particular interest, asthe experimental data about the ether viscosity and theether viscosity measuring methods miss in literature tillnowadays.

218 Yu.M. Galaev

Figure 7: Variation in time of the interference patternbands o�set (calculation)

Let's write down the expression for the value D (t).For this purpose we shall substitute the expressions (11)and (34) in (32) for the values wp (t) and Wc (t) accord-ingly and, allowing the proportions (31), (35), we shallreceive

D (t) � �8lpWh

�c

1Xk=1

�3k J�11 ( k) �

� �exp �� 2ka�2p t�� exp

�� 2ka�2h t��: (40)

In the Fig. 7 in a normalized view the dependencecalculation result D (t) , performed with the expression(40) is given. At calculations the terms number of aseries k = 4, the calculated value of the ether kinematicviscosity is vc = 7 � 10�5m2sec�1 and the followingvalues of the interferometer design parameters are used:ap = 0:0105 m; ah = 0:0367 m; lp = 0:48 m; � =6:5 � 10�7 m.

From the Fig. 7 it follows, that on time expira-tion tm � 0:82 sec, which is digitized from the momentt0 of the beginning time of the interferometer dynam-ic operating regime, the bands o�set maximal value ofthe interference pattern (value D ) should be observed.The anticipated duration of the interferometer dynamicoperating regime matters td � 10:3 sec. Let's use theexpression (40) for specifying the observed value exper-imentally tm � 1 sec. For this purpose we shall substi-tute in (40) the measured value of the ether kinematicviscosity, vea = 6:24 � 10�5 m2sec�1 , we shall receivetm � 0:93 sec. Hence, the calculation results do notcontradict the experience results, which are shown inthe Fig. 6.

The interferometer test results analysis, the etherkinematic viscosity values, calculated and measured,give the basis to consider, that the ether stream proper-ties are close to the stream properties of known gases attheir interaction with solids | to pass aside obstacles

and go in directing systems. It can be suspected, thatsolids (dielectrics, metals etc.) at interaction with theether stream render major ether-dynamic resistance. Itclari�es the interferometer test results, that the tubemade of dielectric can execute the same directing sys-tem role for the ether, as the tube made of metal. Theether stream property, i.e. to pass aside obstacles, couldcause unsuccessful attempts to detect the ether driftwith the devices placed in metallic chambers [17-20,23-26].

For value de�nition of the ether drift horizontalcomponent velocity Wh it is possible to use the bandso�set measured value of an interference pattern at themoment of time tm , when D (tm) = max . From theexpression (40) we shall receive

Wh � D (tm)�c

(8lp

1Xk=1

�3k J�11 ( k) �

� �exp �� 2ka�2p tm�� exp �� 2ka�2h tm

��1: (41)

Let's substitute in (41) the measured values of theether kinematic viscosity vea = 6:24 � 10�5 m2sec�1 ,the value tm = 1 sec, the design parameters valueof the interferometer and calculation parameter (theterms number of a series): ap = 0:0105 m; ah = 0:0367m; lp = 0:48 m; � = 6:5 � 10�7 m; k = 4. In thiscase the measured value of the ether drift horizontalcomponent velocity, will be de�ned as follows

Wh � 525D (tm) : (42)

Let's calculate the minimal value of the ether driftvelocity Whmin , which can be measured with the man-ufactured interferometer, i.e. we shall determine theinstrument sensitiveness. In the part \the interferom-eter test" is marked, that the minimum value Dmin ,which can be digitized with the selected eyefragmentand scale Dmin = 0:05. Then with the expression (42)we shall receive Whmin = 26:25 m/sec.

Let's determine the ether stream regime in the in-terferometer tubes at Wh = Whmin . For this purposewith the expression (4) we shall calculate the minimalvalue of the Reynolds number Remin for the tube withradius ap = 0:0105 m, in which the ether with the vis-cosity vea = 6:24 � 10�5 m2sec�1 moves. Let's receiveRemin � 8834. According to the requirement (3) itcan be written down, that Remin > Rec . Hence, atthe ether drift velocities Wh � 26:25 m/sec the etherstream turbulent regime is possible only in the interfer-ometer tubes.

The optical interferometer tests and tests resultsanalysis give the basis to consider, that the hydrody-namic description of the interferometer operating prin-ciple, reviewed above, is adequate to the imaginationsabout viscous ether stream in tubes, and the manu-factured interferometer is suitable for the ether driftvelocity and the ether kinematic viscosity measuring.


The measurementmethods. The interferometerwas disposed in the country settlement at the height(� 190 m above sea level), in 13 km from Kharkovnorthern suburb. The proximate height (� 200 mabove sea level) is located westward apart 1.7 km. Twopoints were arranged for measurements. The distancebetween them was about 15 m. On the point No 1the interferometer was at the height 1.6 m above theground surface. On the point No 2 it was at the height4.75 m. Two points available, which are located at dif-ferent heights and are practically at the same point ofterrain, it is required for observation of the \height ef-fect." The measurements on the points No 1 and No 2were performed in the open air. On the point No 1 theinterferometer was in surrounding trees shadow and wasnot exposed to direct solar radiation a�ecting within alight day. On the point No 2 the interferometer wasmounted in an umbrella shadow. In winter time theinterferometer was transferred to Kharkov. The pointNo 3 (� 30 m above the ground surface or � 130 mabove sea level) was arranged in the upper level facilityof a bricky house. On the point No 1 the measurementswere carried out in August 2001, on the point No 2 inAugust, September, October and November 2001, onthe point No 3 in December 2001 and in January 2002.

The measurements were carried out cyclically. Onemeasuring cycle lasted 25-26 hours. 2-4 cycles wereperformed within one month. Each cycle contained thefollowing parameters. The interferometer was mountedon a selected point, so that its rotating plain was hor-izontal. After installation the interferometer was keptin new heating environment within one hour (the in-strument was stored in the facility). The measurementswere carried out at each whole hour of stellar time. Onereadout of the measured value was performed under thefollowing schema. The interferometer longitudinal axiswas mounted along a meridian, so that its illumina-tor was turned to the north. The further proceduresdid not di�er from the interferometer operating pro-cedures, which were applied at the �nal stage of theinterferometer test. After the interferometer dynamicregime termination the observer registered the maximalbands o�set value D (tm), as the measured value. Thebands release time to their original position was regis-tered and metered. The interferometer returned to thesteady operating regime. The instrument turned to theinitial position. As a rule, 5-7 readouts were done dur-ing one measuring time (� 10 minutes). The readoutmean value was accepted for the measured value D (S) ,where S is the measuring stellar time.

The processing methods of the measurementresults. The measurement results processing includ-ed the following procedures: values calculations of theether drift horizontal component velocity Wh ; a dailycourse of the ether drift velocity within separate stellarday and the ether drift velocity daily course averagedduring the year epoch Wh (S) ; a daily course of the

ether drift velocity averaged for the whole time of themeasurement series Wh (S) , mean-square value de ec-tion Wh from its mean value �W .

The measurement results were introduced as themeasured value tables D (S) . The values Wh , calculat-ed with the expression (42) were brought to the sametable for each hour of stellar day. Such numbers con-sequence obtained for separate stellar day, describes adaily course Wh (S) .

The mean values of the ether drift velocity and thevalues �W were calculated for each hour of the stellarday with the following known expressions [30]

Wh (S) = ��1�X

j=1

Whj (S); (43)

�W (S) =

8><>:��1

�Xj=1

�Whj (S) � Wh (S)

�2

9=;

1=2

;(44)

where � is the values amount Wh , obtained during thewhole measurement series. The con�dence intervals ofthe measured values were calculated with the knownmethods explained, for example, in the work [30]. Thecalculations were performed with the estimation relia-bility equal to 0.95.

The measurement results. The measurement se-ries results, held since August 2001 till January 2002 arepresented in the work. 2322 readouts of the measuredvalues have been performed during this series. The dis-tribution of readouts amount per months of the year isshown in the table 1

According to the research problems, we shall con-sider this work results along with the experiment re-sults [1-3], [7-9], [10]. These four experiments havebeen performed at various points of a globe with threedi�erent measuring methods: an optical interferome-ter of the �rst order (Europe, Ukraine, 2001{2002 [thiswork]); a radio interferometer of the �rst order, (Eu-rope, Ukraine, 1998{1999 [1-3]); optical interferometersof the second order (Northern America, USA, 1925{1926 [7-9], 1929 [10]). The measuring methods action,which are applied in the above-mentioned experiments,based on wave propagation regularities in movingmedi-um, responsible for these waves propagation, that al-lows to treat the experiment results in the terms of theether drift velocity within the original hypothesis.

The development regularities of viscous mediumstreams ( uids or gases) in directing systems are usedin the work measuring method. The measured valueis proportional to a velocity di�erential of the etherviscous streams in two tubes of di�erent section with-in the original hypothesis. This di�erential value isproportional to the ether drift velocity (the �rst ordermethod).

In the experiment measuring method [1-3] the reg-ularities of viscous medium streams near the surface

220 Yu.M. Galaev

Table 1: Distribution of readouts amount per months of the yearMonth of the year August September October November December January

2001 2001 2001 2001 2001 2002Amount of readouts 792 462 288 312 240 228

Figure 8: Variation of ether drift velocity within a day inAugust epoch

partition are used. The measured value is proportionalto a vertical velocity gradient in the ether drift streamnear the Earth's surface within the original hypothesis.This gradient value is proportional to the ether driftvelocity (the �rst order method).

In the experiments [7-9] and [10] Michelson's cruci-form interferometers were applied. The measured valueis proportional to a velocity di�erential of wave propa-gation in orthogonal related directions in the ether driftstream within the original hypothesis. This di�erentialvalue is proportional to the ether drift velocity (the sec-ond order method).

In the Fig. 8 the experiment results referring toAugust are presented. On fragments of this �gure areshown accordingly: in the Fig. 8a | this work results;in the Fig. 8b | the experiment results [1-3] (the �gureis published for the �rst time); in the Fig. 8c | theexperiment results [7-9].

The ether drift velocities Wh in km/sec. are pend-ing on ordinate axes. The stellar time S in hours is

pending on abscissa axes. Each of the Fig. 8 frag-ments illustrate the variation of the ether drift velocitywithin a stellar day Wh (S) . The experiment resultsare presented only by the authors of work [10] as as-certaining of the velocity maximal value, measured bythem, in relation to the movement W � 6 km/sec, thathas not allowed to show this experiment results in theFig. 8 as the daily dependence Wh (S) . In the Fig. 8the measurement data averaging results were present-ed with the thick lines, which are obtained in each ofthe experiments during August epoch (mean results).The separate observations (measurement results duringa separate day) are shown with thin lines. The dates ofseparate observations are speci�ed on fragments. Theseparate observations on fragments of the Fig. 8a, Fig.8b are selected from the performings, which had thedate, proximate to the date of separate observation ofthe Fig. 8c fragment and which during the day hadno skips during the measuring. The date discrepancyis stipulated also by the fact that the systematic mea-surements in the work began on August 14, 2001, andin the experiment [1-3] | on August 11, 1998.

The positive measurement results, given in the Fig.8, illustrate the development of anisotropy e�ect | theether drift required e�ect. In the work and in the exper-iments [7-9], [10] the anisotropy e�ect was discoveredby the optical interferometer rotation, in the experi-ment [1-3] the opposing radio waves propagation wasapplied.

The similar nature of the ether drift velocity varia-tion within a day in August epoch unite all three frag-ments of the Fig. 8. The �rst minimums in depen-dencies Wh (S) are expressed clearly in all three meanresults. In the work (Fig. 8a) and in the experiment [1-3] (Fig. 8b) temporary position of minimums is S � 3hours. In the experiment [7-9] (Fig. 8c) the temporaryposition of the �rst minimum is S � 0:8 hour. (Suchdiscrepancy in the position of these minimums is about2.2 hour, an explanation has not found yet.) The etherdrift velocity magni�cation is observed during conse-quent 2-3 hours. Further the plateau sites with rathersmall variations of the ether drift velocity in time arenoticed on all fragments. The greatest duration of theplateau site was observed in the experiment [1-3] (Fig.8b), that can be explained by arranging peculiarities ofa radio-frequency spectral line on terrain. In this ex-periment the radio-frequency spectral line is declinedfrom a meridian on 45� to northeast. The variations


of the ether drift apex azimuth (as well as any star az-imuth) occur symmetrically to a meridian line within astellar day. If to take the apex coordinate values intoaccount (according to Miller: � � 65� , a � 17:5h [9]),the ether drift azimuth in this part of a stellar day ac-cepts the values, which lay in the northeast direction,i.e. in the direction close to the direction of a radio-frequency spectral line. In this case the angle betweenthe ether drift azimuth and radio frequency spectralline direction has minimum values. Accordingly at theinterval of 12-16 hours the ether drift radial compo-nent velocity (directed along a radio-frequency spectralline) keeps rather high value, despite of the apex heightmagni�cation (astronomical coordinate). Such arrang-ing peculiarities of the radio interferometer on terraincan explain the relative dependence increase Wh (S) atthe interval of 12-16 hours in comparison with the samedependencies shown on two other fragments. In thework (Fig.8a), according to the accepted measurementmethods, the optical interferometer was located alonga meridian. As the variations of the ether drift azimuthwithin a stellar day occur symmetrically to the merid-ian line, in this case the plateau site duration shouldbe less, than in the experiment [1-3] and less than inthe experiment [7-9] in which the ether drift azimuthvariation was considered by the corresponding rotationof the interferometer.

It can be seen in the Fig. 8a (the mean result ofthe work), that the sites with rather small values ofthe ether drift velocity, extended in time, take placewithin a day. Noticeable bands o�set of an interferencepattern was not observed per a separate day on suchsites. In these cases the ether drift velocity was lowerthan the interferometer sensitiveness (i.e. Wh < 26m/sec), that was used for the interferometer tests, thepurpose of which is given in the above mentioned part"the interferometer test".

Systematic character of experimental investigationsof this work and the works [1-3], [7-9] has shown, thatdependencies measured in one and the same epoch ofthe year Wh (S) , have the similar character of theether drift velocity variation within a day. At the sametime dependencies view Wh (S) , measured in di�erentepochs of the year di�er from each other, that can benoticed, for example, by the experiment published re-sults [7-9]. The reasons of such seasonal variations havenot been de�ned yet. It can be suspected, that magne-tosphere, at its considerable sizes and peculiar shape,ionosphere, the known variations of their state can beresponsible for such dependence variations Wh (S) .

It can be seen in the Fig. 8, the ether drift veloc-ities, measured in each of the experiments, di�er, thatcan be stipulated by the arranging height di�erences ofmeasuring systems above the Earth's surface: 1.6 m;42 m; 1830 m (Fig. 8a, Fig. 8b, Fig. 8c accordingly).The collection of such data illustrates the height e�ectdevelopment. In the work the ether drift velocity mea-

Figure 9: Dependence of the ether drift velocity on theheight above the Earth's surface, � is this work and exper-iment [1-3]; 2 is the experiment [7-9]; � is the experiment[10]

suring have been performed at the heights 1.6 m and4.75 m (position No. 1 and No. 2) for height depen-dence discovery. In the table 2 the mean values of theether drift maximal velocity are given, which are mea-sured in the work and in the experiments [1-3], [7-8],[10]. In these four experiments the measurements areperformed at �ve di�erent heights: 1.6m and 4.75 m inthe work; 42 m in the experiment [1-3]; 265 m and 1830m in the experiment [7-9] (Clevelend and the observa-tory of Mount Wilson accordingly). In the experiment[10] the measurements were carried out also on the ob-servatory of Mount Wilson. However, in contrast withthe experiment [7-9], which was carried out in a lightwooden house, the experiment [10] is performed in afundamental building of an optical workshop of the ob-servatory. It can be supposed, that the ether streambraking by the house walls was the reason of the etherdrift velocity smaller value, measured in the experiment[10] in comparison with the experiment result [7-9].

The table 2 gives the imagination about the etherdrift velocity variation in height band above the Earth'ssurface from 1.6 m up to 1830 m. In the �gure 9 this de-pendence view is presented in the logarithmic scale. Onthe abscissa and ordinates axes the logarithmic valuesof ratios W/W� and Z/Z� were pending accordingly,where: W is the ether drift velocity at the height Z ;the values W� and Z� are considered equal to 1 m/secand 1 m accordingly.

222 Yu.M. Galaev

Table 2: Dependence of the ether drift velocity on the height above the Earth's surfaceThe ether drift velocity (m/sec)

Height above This work The experiment [13] The experiment [79] The experiment [10]the Earth's surface 2001-2002 1998-1999 1925-1926 1929

(meters) Optics Radio waves band Optics Optics1830 { { 10000 6000265 { { 3000 {42 { 1414 { {4.75 435 { { {1.6 205 { { {

It can be seen from the Fig. 9, that di�erent exper-iment results are near one straight line and in heightband from 1.6 m up to 1830 m the ether drift veloci-ty increases with the height growth above the Earth'ssurface. The boundary layer has considerable thick-ness, that can be the consequence of the ether streamand atmosphere interaction. These data do not con-tradict the imaginations of the model [4-6] about theviscous ether and its stream near the Earth's surface.From the table 2, Fig. 8a and the Fig. 9 it can beseen, that the ether drift velocity is rather small nearthe Earth's surface, that can explain the reason of \ze-ro results" of many experimental works, in which thevalue 30 km/sec was taken as the ether drift anticipat-ed velocity. In such experiments the metering devicesensitiveness was obviously poor. With the expression(1) it can be calculated, that at the ether drift velocity200-400 m/sec, the methods of the second order almostare inapplicable for measurements, as in this case suchmethods sensitiveness to the ether drift velocity is lowin 6 orders (!) than the sensitiveness of the �rst ordermethods.

The ether kinematic viscosity has been measuredin the work. The measurement results are explainedabove in the part \Result analysis of the interferom-eter tests," that is stipulated by the peculiarities ofthe experiment implementation. The measured val-ues of the ether kinematic viscosity are in the limitsvea � (5:5 : : :7:1) � 10�5 m2sec�1 . The mean value isequal vea = 6:24 � 10�5 m2sec�1 , that according to thevalue order coincides with the ether kinematic viscosityvalue calculated above vc � 7:06 � 10�5 m2sec�1 .

Hence, the di�erences between the dependenciesWh (S) and the ether drift velocity measured valuesavailable can be explained by the measurement methoddi�erences of the work and the experiments [1-3], [7-9],[10] and di�erences between arranging heights of mea-suring systems. The results of four experiments do notcontradict each other, that illustrate the reproducedmeasurement nature of the ether drift e�ects in variousexperiments performed in di�erent geographic condi-tions with di�erent measurement methods applying.

Figure 10: The mean daily course of the ether drift velocity


According to the original hypothesis, the ether driftvelocity horizontal component Wh should change itsvalue with the period per one stellar day (the space ef-fect). For revealing the ether drift velocity componentwith such period, the results of systematic measure-ments were subjected to statistical processing in stellartime scale. The results of such processing are shownin the Fig. 10. On the fragments of the Fig. 10 thestellar time S in hours is suspended on the abscissaaxes, the ether drift velocity value Wh in km/sec issuspended on the ordinate axes. The vertical hatch-es indicate the con�dence intervals. In the Fig. 10athe mean daily course of the ether drift velocity with-in a stellar day Wh (S) is given. This dependence iscalculated according to the measurement results of thework, which were performed during �ve months of theyear, since September 2001 till January 2002. During�ve months the numerical value of stellar time shifts re-garding to the solar time in 10 hours. Since Septembertill November the measurements were performed on thepoint No2. In December and January | on the pointNo3. The mean values are calculated with the expres-sion (43). For comparison, in the Fig. 10b the meanresult is given, which was obtained in the experiment[1-3] during year's �ve months of the same name, sinceSeptember 1998 till January 1999 (Here, as contrast-ed to the similar �gure, given in the works [1-3], themeasured value is expressed in the ether drift velocityvalues.) In the works [7-9], [10] such data miss, owingto smaller on coverage of year's epochs of the measure-ment statistics in these experiments.

Both fragments of the Fig. 10 as a whole have sim-ilar nature of the ether drift velocity variation withina day. The di�erences in the curve shapes can be ex-plained by viscous ether stream interaction with theterrain relief elements, which in these di�erent experi-ments had the distinguished performances and featuresof radio-frequency spectral line arranging on terrain inthe experiment [1-3]. On the fragment of the Fig. 10a(this work), as contrasted to the result of the exper-iment [1-3] (Fig. 10b), the ether drift velocities havesmaller values, that can be explained by the heightdistinction of measuring points in these experiments.The dependencies Wh (S) have the forms of periodical-ly changed values with the periods equal to a stellarday, that can be explained by a space (galactic) originof the ether drift. In the work, the observed bands o�-set direction of an interference pattern corresponded tothe ether drift northern direction at measurement im-plementation. Hence, the results of the work do notcontradict the experiment results [1-3], [7-9], [10] andimaginations of the works [4-6] about the northern posi-tion of the ether drift apex, that demonstrate the repro-duced result nature of the ether drift e�ects measure-ment in di�erent experiments, performed with di�erentmeasuring methods application.

In the work we shall be con�ned to qualitative com-parison of the work results with the experiment data[1-3], [7-9], [10]. For conducting of quantitative compar-ative analysis it is necessary to specify the ether driftapex coordinate values on the celestial sphere, which forthe �rst time were determined in the experiment [7-9],to specify an analytical view of the ether drift veloci-ty dependence on the height above the Earth's surfaceproposed in the works [1-3], to elaborate the calcula-tion method of the terrain relief in uence on the etherstreams forming near the Earth's surface, to determineprobable in uencing of the Earth magnetosphere andionosphere, that is the subject of separate investigationsand goes out the frame of the work problems. Due tothe reason this experiment results, the experiment [1-3]and the experiment [7-9] are given without any correc-tion, though its usefulness at the result comparison ofdi�erent experiments is quite obvious.

Thus, in the work, the hypothesis experimental veri-�cation about the ether existence in nature, i.e. materi-al medium, responsible for electromagnetic waves prop-agation, in the optical wave band has been performed.The estimation of the ether kinematic viscosity valuehas been performed. The �rst order optical methodfor the ether drift velocity and the ether kinematic vis-cosity measuring has been proposed and realized. Themethod action is based on the development regularitiesof viscous liquid or gas streams in the directing sys-tems. The signi�cant measurement results have beenobtained statistically. The development of the etherdrift required e�ects has been shown. The measuredvalue of the ether kinematic viscosity on the value or-der has coincided with its calculated value. The velocityof optical wave propagation depends on the radiationdirection and increases with height growth above theEarth's surface. The velocity of optical wave propaga-tion changes its value with a period per one stellar day.The detected e�ects can be explained by the following:

| optical wave propagation medium available re-garding to the Earth's movement;

| optical wave propagation medium has the viscos-ity, i.e. the feature proper to material mediums com-posed of separate particles;

| the medium stream of optical wave propagationhas got a space (galactic) origin.

The work results comparison to the experiment re-sults, executed earlier in order of the hypothesis veri-�cation about the existence of such material mediumas the ether in nature, has been performed. The com-parison results have shown the reproduced nature ofthe ether drift e�ect measurements in various experi-ments performed in di�erent geographic requirementswith di�erent measurement methods application.

The work results can be considered as experimen-tal hypothesis con�rmation about the ether existencein nature, i.e. material medium, responsible for elec-tromagnetic waves propagation.

224 Yu.M. Galaev

References

[1] Yu. M. Galaev. \Ether-drift e�ects in the experimentson radio wave propagation." Radiophysics and electron-ics, 2000, Vol. 5, No.1, pp. 119{132. (in Ukraine).

[2] Yu. M. Galaev. \Ether-drift. Experiment in the bandof radio wave." Zhukovsky: Petit, 2000, 44 pp. (in Rus-sia).

[3] Yu. M. Galaev. \Etheral wind in experience ofmillimetric radiowaves propagation." Spacetime &Substance, 2001, Vol. 2, No. 5(10), pp. 211{225,http://www.spacetime.narod.ru/0010-pdf.zip.

[4] W. Azjukowski. \Dynamik des �Athers." Ideen des ex-akten Wissens., Stuttgart, 1974, Nu. 2, s. 48{58.

[5] V.A. Atsukovsky. \The introduction into etherdynam-ics. Model imaginations of material and �eld structureson the basis of gas like ether." Moskow, MOIP physicsdep., 1980, Dep. in VINITI 12.06.80 No. 2760-80 DEP.(in Russia).

[6] V.A. Atsukovsky. \General ether-dynamics. Simulationof the matter structures and �elds on the basis ofthe ideas about the gas-like ether." Energoatomizdat,Moscow, 1990, 280 pp. (in Russia).

[7] D.C. Miller. \Ether drift experiments at Mount Wilsonsolar observatory." Phys. Rev., 1922, Vol. 19, pp. 407{408.

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

[9] D.C. Miller. \Signi�cance of the ether-drift experi-ments of 1925 at Mount Wilson." Science., 1926, Vol.68, No. 1635, pp. 433{443.

[10] 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., 1929, Vol. 18, No. 3, pp. 181{182.

[11] E.T. Whittaker. \A History of the Theories of Aetherand Electricity." Izhevsk: RIC Regular and randomdynamics, 2001, 512 pp. (in Russia). E.T. Whittaker.\A History of the Theories of Aether and Electricity."Thomas Nelson and Sons Ltd, Edinburgh, 1953.

[12] A.A. Michelson. \The relative motion of the Earth andthe Luminiferous ether." The American Journal of Sci-ence., 1881, III series, Vol. 22, No. 128, pp.120{129.

[13] G.G. Petrash, S.G. Rautian. \Michelson's Interferome-ter." In the book \Physical encyclopaedic vocabulary."The Soviet encyclopedia, Moskow, 1962, Vol. 2, pp.202{203 (in Russia).

[14] A.A. Michelson, E.W. Morley. \The relative motion ofthe Earth and the luminiferous aether." The AmericanJournal of Science. Third Series., 1887, Vol. 34, pp.333{345; Philosophical journal., 1887, Vol. 24, pp. 449{463.

[15] W.I. Frankfurt, A.M. Frank. \Optics of moving media."Nauka, Moskow, 1972, 212 pp. (in Russia).

[16] S.I. Vavilov. \New searchs of \the ether drift"." Suc-cesses of physical sciences, 1926, Vol. 6, pp. 242{254(in Russia).

[17] R.J. Kennedy. \A re�nement of the Michelson-Morleyexperiment." Proc. Nat. Acad. Sci. of USA., 1926, Vol.12, pp. 621{629.

[18] K.K. Illingworth. \A repetition of the Michelson-Morley experiment using Kennedy's re�nement." Phys-ical Review., 1927, Vol. 30, pp. 692{696.

[19] E. Stahel. \Das Michelson-Experiment, ausgefurt imFreiballon." \Die Naturwissenschaften," Heft 41, 1926,B8, Nu. 10, S. 935{936.

[20] Joos G. Die Jenaer. \Widerholung des Mihelsonver-suchs." Ann. Phys., 1930, B7, S. 385{407.

[21] \Ether-drift," Digest by Dr. in Sc. V.A. Atsukovsky.Energoatomizdat, Moskow, 1993, 289 pp. (in Russia).

[22] D.C. Miller. \The ether-drift experiment and the de-termination of the absolute motion of the Earth." Rev.Modern. Phys., 1933, Vol. 5, No. 3, pp. 203{242.

[23] L. Essen. \A new ether drift experiment." Nature.,1955, Vol. 175, pp. 793{794.

[24] J.P. Cedarholm, G.F. Bland, B.L. Havens, C.H.Townes. \New experimental test of special relativity."Phys. Rev. Letters., 1958, Vol. 1, No. 9. pp. 342{349.

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

[26] T.S. Jaseja, A. Javan, J. Murbeam, C.H. Townes. \Testof special relativity or space isotropy by use of infraredmasers." Phys. Rev., 1964. Vol. 133a, pp. 1221{1225.

[27] L.G. Loytsyansky. \Mechanics of uid and gas." Nauka,Moskow, 1973, 848 pp. (in Russia).

[28] N.A. Slezkin. \Dynamics of viscous incompressible u-id." Gostechizdat, Moskow, 1955, 520 pp. (in Russia).

[29] S.G. Rautian. \Rozhdestvensky's Interferometer." Inthe book \Physical encyclopaedic vocabulary." The So-viet encyclopedia, Moskow, 1962, Vol. 2. p. 203 (in Rus-sia).

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


ON THE BASIS FOR GENERAL RELATIVITY THEORY

S.N. Arteha1

Space Research Institute, Profsoyuznaya 84/32, Moscow 117997, Russia

Received December 23, 2002

The basic concepts of the general relativity theory (GRT), such as space, time, the relativity of simultaneity, aresystematically analyzed. The logical inconsistencies of basic GRT notions are indicated. Many disputable andcontradictory points of this theory and its corollaries are considered in detail.

1. Introduction

A series of logical paradoxes has been analyzed in de-tail in [1-3], and the complete experimental and logicalgroundlessness of SRT was demonstrated. Unlike SRT,the GRT contains some rather interesting ideas, suchas the principle of equivalence expressed via the idea of\geometrization." If it's basis were true, the GRT couldhave a claim on status of a hypothesis about some cor-rection to the static Newton's law of gravitation. Sinceit is not the case, the gravitation theory must be con-structed in a di�erent manner.

The basic purpose of this work is the criticism ofbasis notions of GRT; it is contained in Section 2. Alogical inconsistency of space and time notions in GRTis demonstrated here. The plausible errors and dis-putable points from the textbooks [4-6] are displayedstep by step. The time synchronization issues and theMach principle are also discussed, and the attention isgiven to doubtful corollaries from GRT. Section 3 con-tains the conclusions.

2. Criticism of GRT Fundamentals

Many GRT inconsistencies are well-known: 1) the prin-ciple of correspondence is violated (the limiting transi-tion to the case without gravitation can not exist with-out introducing the arti�cial external conditions); 2)the conservation laws are absent; 3) the relativity of ac-celerations contradicts the experimental facts (rotatingliquids under space conditions have the shape of ellip-soids, whereas non-rotating ones - the spherical shape);4) the singular solutions exist. (Usually, any theory isconsidered to be inapplicable in similar cases, but GRTfor saving its \universal character" begins to constructfantastic pictures, such as black holes, Big Bang, etc.).

Let us consider the general claims of the GRT. Webegin with the myth \on the covariance." The unam-


biguous solution of any di�erential equation is deter-mined, except the form of the equation, also by spec-i�cation of the initial and/or boundary conditions. Ifthey are not speci�ed, then, in the general case, thecovariance either does not determine anything, or, atchanging the character of the solution, can even resultin a physical nonsense. If, however, the initial and/orboundary conditions are speci�ed, then with substitu-tion of the solutions we obtain the identities, which willremain to be identities in any case for any correct trans-formations. For any solution it is possible to invent theequations, which will be invariant with respect to somespeci�ed transformation, if we properly interchange theinitial and/or boundary conditions.

The analogies with subspaces are often used in theGRT; for example, a rolled at sheet is considered.However, the subspace cannot be considered separatelyfrom the space as a whole. For example, in rolling asheet into a cylinder the researcher usually transfers,for convenience, into the cylindrical coordinate system.However, this mathematical manipulation does not in- uence at all the real three-dimensional space and thereal shortest distance.

The simplicity of postulates and their minimumquantity do not still guarantee the correctness of thesolution: even the proof of equivalence of GRT solu-tions is a di�cult problem. The number of prerequisitesshould be, on one hand, su�cient for obtaining a cor-rect unambiguous solution, and, on the other hand,it should provide wide possibilities for choosing mathe-matical methods of solution and comparison (the math-ematics possesses its own laws). The GRT, along witharti�cial complication of mathematical procedures, hasintroduced, in fact, the additional number of \hidden�tting parameters" (from metrical tensor components).Since the real �eld and metrics are unknown in GRTand are subject to determination, the result is simply�tted to necessary one with using a small amount ofreally various experimental data.

Whereas in SRT though an attempt was made to

226 S.N. Arteha

con�rm the constancy of light speed experimentally andto prove the equality of intervals theoretically, in GRTeven such attempts have not been undertaken. Since in

GRT the integralR ba dl is not meaningful in the general

case, since it can depend on the path of integration,all integral quantities and integral-involving derivationscan have no sense.

A lot of questions cause us to muse. If the gener-al covariance of equations is indispensable and unam-biguous, then what could be the limiting transition toclassical equations, which are not generally covariant?What is the sense of gravitation waves, if the notion ofenergy and its density is not de�ned in GRT? Similarly,what is meant in this case by the group velocity of light(and by the �niteness of a signal transmission rate)?

The generality of conservation laws does not dependon the method of their derivation (either by means oftransformations from the physical laws or from symme-tries of the theory). The obtaining of integral quantitiesand the use of integration over the surface can lead todi�erent results in the case of motion of the surface (forexample, it can depend on the order of limiting tran-sitions). The absence in GRT of the laws of conser-vation of energy, momentum, angular momentum andcenter of masses, which have been con�rmed by numer-ous experiments and have \worked" for centuries, causeserious doubts in GRT (following the principle of con-tinuity and eligibility of the progress of science). TheGRT, however, has not yet built up a reputation foritself in anything till now, except globalistic claims onthe principally unveri�able, by experiments, evolutionof the Universe and some rather doubtful �ttings undera scarce experimental base. The following fact causeseven more doubt in GRT: for the same system (and onlyof \insular" type) some similarity of the notion of en-ergy can sometimes be introduced with using Killing'svector. However, only linear coordinates should be usedin this case, but not polar ones, for example. The aux-iliary mathematical means can not in uence, of course,the essence of the same physical quantity. And, �nally,the non-localizability of energy and the possibility ofits spontaneous non-conservation even in the Universescales (this is a barefaced \perpetuum mobile") causeus to refuse from GRT completely and either to revisethe conception \from zero," or to use some other de-veloping approaches. Now we shall pass from generalcomments to more speci�c issues.

The question on the change of space geometry inGRT is fully aberrant. The �niteness of the rate oftransmission of interactions can change only physical,but not mathematical laws. Whether shall we assert,that the straight line does not exist, only because itsdrawing into in�nity, even at light speed, will require in-�nite time? (The same is true for the plane and space).The mathematical sense of derivatives can not changeas well. One of GRTdemonstrations \on the inevitabili-

ty of the change of geometry in the non-inertial system"is as follow: in the rotating coordinate system, due tocontraction of lengths, the ratio of the length of a circleto its diameter will be lower, than � . In fact, however,not only the true, but even the observed geometry willnot change: whether the mathematical line will moveor change as we move? Suppose at �rst, that the circlewill move radially. Let we have three concentric circlesof almost the same radius. We place the observers onthese circles and number them in the order from thecenter: 1, 2, 3. Let the second observer be motionless,whereas �rst and third ones are rotating around centerO clockwise and counter-clockwise at the same angu-lar velocity. Then, owing to the di�erence in relativevelocities and contraction of lengths, the observers willinterchange their places. However, when they happento be at the same point of space, they will see di�erentpictures. Indeed, the 1-st observer will see the follow-ing position from the center: 3, 2, 1, whereas the 2-ndobserver will see the di�erent order: 1, 3, 2, and onlythe 3-rd observer will see the original picture: 1, 2, 3.So, we have a contradiction. Suppose now, that thegeometry of a rotating plane has changed. However,what will be more preferable in such a case: the topor the bottom? The problem is symmetric, in fact; towhat side the plane has curved in such a case? If wemake the last supposition, that the radius has curved(as the apparent motion changes in the non-inertial sys-tem), then the second observer will see it as non-curved,whereas the �rst and third observers will consider it as\curved" to di�erent sides. Thus, three observers willsee di�erent pictures at the same point for the samespace; therefore, the curvature of the radius is not anobjective fact.

The rotating circle proves the contradictive natureof SRT and GRT ideas. Really, according to the text-books, the radius, which is perpendicular to the motion,does not change. Therefore, the circles will remain attheir places irrespective of the motion. Let us seat theobservers on a motionless circle at equal distances fromeach other and produce a point-like ash from the cen-ter of a circle, in order the observers to draw the strokeson moving circles. Owing to the symmetry of a prob-lem, the strokes will also be equidistant. At subsequentperiodic ashes each observer will con�rm, that a strokemark passes by him at the ash instant, that is, thelengths of segments of motionless and rotating circlesare equal. When the circles stop, the marks will remainat their places. The number of equidistant marks willnot change. Therefore, the lengths of segments will beequal in the motionless case as well. Thus, no contrac-tion of lengths and change of geometry took place atall.

Now we consider again the space geometry problem.This problem is entirely confused still since the times ofGauss, who wanted to determine the geometry with thehelp of light beams. The limited nature of any experi-

On the Basis for General Relativity Theory 227

LA B

C

g

Figure 1: \Geometry of a triangle"

ment can not in uence the ideal mathematical notions,does it? Note, that in GRT the light even moves notalong the shortest path: instead of Fermat's principle�Rdl = 0, we have in GRT [4]: �

R(1=pg00)dl = 0,

where g�� is metric tensor. What does distinguish thelight in such a case? The necessity of changing the ge-ometry is often \substantiated" in textbooks as follows:in order the light to \draw" a closed triangle in the grav-itational �eld, the mirrors should be turned around atsome angle; as a result, the sum of angles of a trianglewill di�er from � . However, for any point-like bodyand three re ectors in the �eld of gravity (see Fig. 2)the sum of \angles" can be written as:

X�i = � + 4arctan

gL

2v20

!� 2 arctan

gL

v20

!:

It occurs, that the geometry of one and the same spacedepends on the conditions of the experiment: on L andv0 . Since the angle � between the mirrors A and Bcan also be changed, we have a possibility of arti�cialchanging the geometry within wide limits. Note, thatthe same variable parameters � and L remain for thelight as well. In such \plausible" proofs of the neces-sity of changing the geometry some important pointsare not emphasized. First, both in the experiment withmaterial points, and in the experiment with the lightthe geometry is \drawn" sequentially during some time,rather than instantaneously. Second, for acceleratedsystems the particles (and the light) move in vacuumrectilinearly, according to the law of inertia, and, ac-tually, the motion of the boundaries of this acceleratedsystem is imposed on this motion additively. All an-gles of incidence (in the laboratory system) are equalto corresponding angles of re ection, and the \geome-try of angles" does not change at all. Simply, the �gureis obtained unclosed because of motion of the bound-aries. Third, the role of the boundaries is not uncoveredat all in determining the relations between the lengths

of real bodies. For example, if all points of a real bodyare subject to the e�ect of identical accelerating force,then the mutual relation between lengths and angles(\the geometry") remains unchanged. If, however, on-ly the boundaries are subject to acceleration, then allreal changes of bodies' size take place only at interac-tion with the boundaries. In any case the Euclideanstraight lines can be drawn. For example, to draw thehorizontal straight line in the gravitational �eld we taketwo similar long rods. At the middle of the �rst rod weinstall a point-like support. As a result of bending ofa rod, the upward-convex line is generated. Then weinstall two point-like supports for the second rod at thelevel of two lowered ends of the �rst rod. As a result ofbending of the second rod, the downward-convex line isgenerated. The middle line between these two bondedrods determines the straight line.

Now we shall turn to the next important GRT no-tion - the equivalence of the gravitational �eld to somesystem non-inertiality. In contrast to any non-inertialsystem, the gravitational �eld possesses some uniqueproperty: all moving objects de ect in it toward a sin-gle center. If we generate two light beams between twoideal parallel mirrors and direct them perpendicular tomirrors, then in the inertial system these beams willmove parallel to each other for in�nitely long time. Asimilar situation will take place at acceleration in thenon-inertial system, if the mirrors are oriented perpen-dicular to the direction of acceleration. And, on thecontrary, in the gravitational �eld with similar orienta-tion of mirrors the light beams will begin to approacheach other. And, if some e�ect will happen to be mea-sured during the observation, then, owing to a greatvalue of light speed, the existence of namely the gravi-tational �eld (rather than the non-inertiality) can alsobe found. Obviously, the curvature of mirrors shouldnot be taken into consideration, since, along with grav-itational forces there exist also the other forces, whichcan retain the mutual con�guration of mirrors. The dis-tinction of a spherical symmetry from planar one canbe found for weak gravitational �elds as well. The GRTconclusion on the possibility of excluding the gravita-tional �eld for some inertial system during the wholeobservation time is wrong in the general case.

The equivalence principle of the gravitational �eldand acceleration can be related to one spatial point on-ly, i.e. it is unreal (it leaded to a false result for the lightbeam de ection, for example). The equivalence princi-ple of the inertial and gravitating mass can be rigorous-ly formulated also for a separate body only (it is unrealfor GRT, since GRT involves interdependence of thespace-time and all bodies). Because of this, GRT doesnot physically proceed to any non-relativistic theory atall (but formally mathematically only). All relativisticlinear transformations can be related to empty spaceonly, since real bodies (even as reference points) leadto nonlinear properties of the space. Then, phenome-

228 S.N. Arteha

na di�erences with changing reference systems must bestudied for the same point (in the space and time). Buthow can two di�erent observers be placed at one point?Therefore, the relativistic approach can possess the ap-proximate model character only (without globality).

It is not any surprising thing, that the same physicalvalue - a mass - can participate in di�erent phenomena:as a measure of inertia (for any acting forces, includ-ing the gravitational one) and as a graviting mass (forexample, a moving charge produces both electric andmagnetic �elds). The question on the rigorous equalityof inertial and gravitating massess is entirely arti�cial,since this equality depends on the choice of a numeri-cal value of the gravitational constant . For example,expressions (laws) retain the same form in the case ofproportionality mg = �min , but the gravitational con-stant will be de�ned as 0 = �2 . It is not necessaryto search any mystics and to create pictures of curvedspace. The substitution of the same value (for the in-ertial and gravitating mass) is made not only for GRT,but for the Newton's theory of gravitation as well. It isnothing more than an experimental fact.

When one comes to the dependence of a form ofequations on space-time properties [7], there existssome speculation for this idea. The impression is giventhat we can change this space-time to check the de-pendence claimed. In fact, the Universe is only one(unique). GRT tries to add a complexity of the Uni-verse to any local phenomena, which is not positivefor science. The choice of local coordinates is a di�er-ent matter (a phenomenon symmetry can simplify thedescription) and globality is not the case again.

The use of non-inertial systems in GRT is contra-dictory intrinsically. Really, in a rotating system ratherdistant objects will move at velocity greater than lightspeed; but SRT and GTR assert, that the apparentvelocities should be lower, than c . However, the ex-perimental fact is as follows: the photograph of thesky, taken from the rotating Earth, indicates, that thevisible solid-state rotation is observed. The use of a ro-tating system does not contradict the classical physicsat any distance from the center, whereas in GRT thevalue of g00 component becomes negative (but this isinadmissible in GRT).

The notion of time in GRT is confused beyond thelimit as well. What does it mean by the clock syn-chronization, if it is possible only along the unclosedlines? The change of time reference point in movingaround a closed path is an obvious contradiction ofGRT, since at a great synchronization rate many simi-lar passes-around can be made, and arbitrary aging orrejuvenation can be obtained. For example, consideringthe vacuum (emptiness) to be rotating (if we ourselvesshall move around a circle), we can get various resultsdepending on a mental idea.

Using the modi�ed paradox of twins [1], the inde-pendence of time on acceleration can easily be proven.

Let two astronauts - the twins - are at a great distancefrom each other. On a signal of the beacon, situated atthe middle, these astronauts begin to y toward a bea-con at the same acceleration. Since in GRT the timedepends on the acceleration and the acceleration hasrelative character, each of the astronauts will believe,that his twin brother is younger than he is. At meetingnear the beacon they can exchange photos. However,owing to the problem symmetry, the result is obvious:the time in an accelerated system ows at the same rate,as in non-accelerated one. If we suppose the gravita-tional �eld to be equivalent to the acceleration (accord-ing to GRT), then we obtain, that the time intervals donot depend on the gravitational �eld presence.

Now we make some remarks concerning the methodof synchronization of times by means of a remote pe-riodic source disposed perpendicular to the motion ofa body [1]. We begin with inertial systems. The pos-sibility of time synchronization on restricted segmentsmakes it possible to synchronize the time throughoutthe line of motion. Indeed, if for each segment thereexists an arbitrarily remote periodic source sending thefollowing information: its number Nj , the quantity njof passed seconds (the time reference point is not co-ordinated with other sources), then the observers atjunctions of segments can compare the time referencepoint for a source on the left and for a source on theright. Transmitting this information sequentially fromthe �rst observer to the last one, it is possible to estab-lish a single time reference point (the time itself, as itwas shown in [1], has absolute sense).

Apparently, the observed rate of transmission ofsynchronization signals has no e�ect on the determina-tion of duration of times: the pulses (for example, lightspheres or particles), which mark the number of passedseconds, will equidistantly �ll the whole space, and thenumber of spheres emitted by a source will be equalto the number of spheres, which intersect the receivingobserver. (We are not the gods, you see, to be ableto introduce the \beginning of times": the time takesalready its normal course and elapses uniformly.) Evenif we consider the apparent signal propagation rate tobe c = c(r), then, irrespective of the path of light, thenumber of spheres reached the receiving observer (hav-ing a zero velocity component in the source direction)will be the same as the number of spheres emitted by asource (simply, the spheres can be spatially thickenedor rare�ed somewhere). Thus, the full synchronizationis possible in the presence of spatial inhomogeneities (ofthe gravitational �eld) as well.

In physics it is not accepted to take into accountthe same e�ect twice. It is clear, that the accelera-tion and gravitation express some force, that in uencesvarious processes. But this will be the general resultof the e�ect of namely the forces. For example, notany load can be withstood by a man, the pendulumclock will not operate under zero gravity, but this does


not mean, that the time stopped. Therefore, the roughHafele-Keating's experiment states the trivial fact, thatthe gravitation and acceleration somehow in uence theprocesses in a cesium atomic watch, and the high rela-tive accuracy of this watch is fully groundless for a �xedsite. Besides, interpretation of this experiment contra-dicts the \explanation" of the Pound-Rebka's experi-ment with supposition about independence of frequen-cy of emission in \the units of intrinsic atom time" [5]on gravitational �eld. Besides, a further uncertainty inGRT must be taken into consideration: there can ex-ist immeasurable rapid �eld uctuations (with a rategreater than inertness of measuring instruments) evenin the absence of the mean �eld g . Such the uncertain-ty exists for any value of g : since the time in GRT doesnot depend on g -direction, then an e�ective potentialwill be nonzero even with < g >= 0. Whether is itpossible to invent, though theoretically, a precise watch,which can be worn by anybody? Probably, a rotating ywheel with a mark (in the absence of friction - ona superconducting suspension), whose axis is directedalong the gravitational �eld gradient (or along the re-sultant force) could read out the correct time. At least,no obvious reasons and mechanisms of changing the ro-tation rate are seen in this case. Certainly, for weakgravitation �elds such a watch will be less accurate atthe modern stage, than cesium one. We hypothesize,that atom decay is anisotropic, and this anisotropy canbe interrelated with a direction of the atomic magneticmoment. In this case we can regulate atomic momentsand freeze the system. Then, the \frozen clock" willregister di�erent time depending on its orientation inthe gravitational �eld.

Now we return to synchronizing signals (for simul-taneous measurement of lengths, for example). For arectilinearly moving, accelerated system it is possibleto use the signals from a remote source being perpen-dicular to the line of motion, and for the segment ofa circle the source can be at its center. These casesactually cover all non-inertial motions without gravi-tation. (Besides, for the arbitrary planar motion it ispossible to make use of a remote periodic source beingon a perpendicular to the plane of motion.) For thereal gravitational �eld of spherical bodies in arbitrarymotion along the equipotential surfaces it is possible touse periodic signals issuing from the gravitational �eldcenter.

Note, that to prove the inconsistency of SRT andGRT conclusions on the change of lengths and timeintervals it is su�cient, that the accuracy of ideal mea-surement of these values could principally exceed thevalue of the e�ect predicted by SRT and GRT. For ex-ample, for a source being at the middle perpendicularto the line of motion we have: �t = l2=(8Rc); thatis, �t can be decreased not only by choosing the greatradius of a light sphere, but also by choosing a smallsection of motion l . From the SRT formulas on time

contraction we have: �t = l(1�p1� v2=c2)=v . If for�nite R and speci�ed speed v we choose such l , thatthe inequality

l=(8Rc) < (1�p1� v2=c2)=v; (1)

be met, then the conclusions of relativistic theories oc-cur to be invalid.

For the system arbitrarily moving along the radius(drawn from the gravitational �eld center) it is possibleto use for synchronization a free falling periodic sourceon the perpendicular to the line of motion. In this caseR should be chosen of such value, that the �eld can notactually change (due to equipotential sphere rounding)at this distance, and corresponding l from (1) near thepoint, to which the perpendicular is drawn. Therefore,the GRT conclusions can be refuted in this case as well.For the most important special cases the \universal"SRT and GRT conclusions on the contraction of dis-tances as a property of the space itself are invalid. Inthe most general case it seems intuitively quite obvious,that such a position of a periodic source can be found,that the signal to come perpendicular to the motion,and that such R and l from (1) to exist, which re-fute the GRT results. There is no necessity at all in a\spread" frame of reference and in an arbitrarily oper-ating clock: any change of real lengths should be ex-plained by real forces; it is always possible to introducea system of mutually motionless bodies and the univer-sal time. Thus, the space and time must be Newtonianand independent on the motion of a system.

Now we pass to mathematical methods of GRT andto corollaries of this theory. The games with the space-time properties result in the fact, that in GRT the appli-cation of variation methods occurs to be questionable:the quantities are not additive, the Lorentz transfor-mations are non-commutative, the integral quantitiesdepend on the path of integration. Even it is not clear,how the terminal points can be considered as �xed, ifthe distances are di�erent in di�erent frames of refer-ence.

Because of nonlocalizableness (non-shieldness) ofgravitation �eld, conditions on in�nity (because of themass absence on in�nity, it is euclideanness) are prin-cipally important for the existence of the conservationlaws [7] (for systems of the insular type only). Theclassical approach is more successive and useful (the-oretically and practically): energy is determined cor-rectly to a constant, since the local energy di�erencebetween two transition points has a physical meaning(therefore, conditions on in�nity is groundless).

Highly doubtful is the procedure of linearization inthe general form, since it can be only individual. Thetending to simplicity is declared, but even two timesare introduced - coordinate and intrinsic ones. The �t-ting to the well-known or intuitive (classically) resultis often made. So, for motion of Mercury's perihelion[5] the du=d' derivative can have two signs. Which

230 S.N. Arteha

of them should be chosen? To say already nothing ofthe fact, that the dividing by du=d' is performed, butthis quantity can be zero. Calculating the periheliondisplacement in GRT (from the rigorous solution fora single attractive point), the impression is given thatwe know astronomical masses exactly. If we use GRTas a correction to Newton's theory, the situation is infact opposite: there exists a problem knowing visibleplanet motions to reestablish the exact planet masses(to substitute the latters and to check GRT thereafter).Imagine the circular planet orbit. It is obvious in thiscase, that the Newtonian rotation period will alreadybe taken with regard to an invisible precession, i.e. theperiod will be renormalized. Therefore, renormalizedmasses are already included in Newton's gravitationtheory. Since the GRT-corrections are much less thanthe perturbation planet actions and the in uence of anon-sphericity, the reestablishment of exact masses canessentially change the description of a picture of themotion for this complex many-body problem (see otherobjections [2]). No such detailed analysis was carriedout. The complexity of spatial-temporal links is stat-ed, but eventually one passes for a very long time tocustomary mathematical coordinates; otherwise thereis nothing to compare the results with. For what wasthere a scrambling?

The prototype of the \black hole" in Laplac's solu-tion, where the light, moving parallel to the surface,begins to move over a circle like the arti�cial satel-lite of the Earth, di�ers from the GRT ideas. Noth-ing prohibits the light with a rather high energy toescape the body in the direction perpendicular to itssurface. There is no doubt, that such beams will exist(both by internal and external reasons): for example,the beams falling from outside will be able to accumu-late energy, in accordance with the energy conservationlaw, and to leave such a \black hole" after re ecting.\The black holes" in GRT is a real mysticism. If wetake a long rod, then at motion its mass will increaseand the size will decrease (according to SRT). Whatwill happen? Is \the black hole" generated? All thesky will become �lled with \black holes," if we shallmove rapidly enough. And, you see, this process wouldbe irreversible.

The presence of singularities or multiple connectionof the solution implies, that, as a minimum, the solutionis inapplicable in these regions. Such a situation takesplace with the change of the space - time signature forthe \black hole" in the Schwarzschild solution, and it isnot necessary to search any arti�cial philosophical sensein this situation. The singuliarity in the Schwarzschildsolution for r = rg cannot be eliminated by purelymathematical manipulations: the addition of the in-�nity with the other sign at this point is the arti�cialgame with the in�nities, but such a procedure requiresthe physical basis. (You see, the singularity at zero isnot eliminated by arti�cial addition of � exp (��r)=r ,

where � is a large quantity).Even fromGRT follows the impossibility of observa-

tion of \black holes": the time of \the black hole" for-mation will be in�nite for us as remote observers. Andsince the collapse cannot be completed, the solutions,which consider all things as though they have alreadyhappened, have no sense. The separation of eventsby in�nite time for internal and external observers isnot \an extreme example of the relativity of the timecourse," but the elementary manifestation of the in-consistency of Schwarzschild's solution. The same factfollows from \the incompleteness" of systems of solu-tions. It is not clear, what will happen with the chargeconservation law, if a greater quantity of charges of thesame sign will enter \the black hole"? The mysticaldescription of \metrical tidal forces" [6] at approaching\the black hole" is invalid, since it would mean, thatthe gravitation force gradient is great within the limitsof a body, but all GRT ideas are based on the oppo-site assumptions. The Kerr metric in the presence ofrotation also clearly demonstrates the inconsistency ofGRT: it gives in a strict mathematical manner severalphysically unreal solutions (the same operations, as forSchwarzschild's metric, do not save the situation).

GRT contains a lot of doubtful prerequisites andresults. List some of them. For example, the require-ment of gravitational �eld weakness for low velocities isdoubtful: if the spacecraft is landed on a massive plan-et, whether it can not stand or slowly move? Whethersome molecules with low velocities cannot be found inspite of temperature uctuations? The considerationof a centrally symmetric �eld in GRT has not physicalsense as well: since the velocity can be only radial, thennot only rotations, but even real temperature charac-teristics can not exist (i.e. T = 0K ). The �eld ina cavity is not obtained in a single manner, but, sim-ply, two various constants are postulated in order toavoid singularities. The emission of gravitation wavesfor a parabolic motion (with eccentricity e = 1) resultsin the in�nite loss of energy and angular momentum,which obviously contradicts the experimental data. Infact, GRT can be applied only for weak �elds and weakrotations, i.e. in the same region, as the Newtoniantheory of gravitation. Recall that the interaction be-tween moving charges di�ers from the static Coulomblaw. Therefore, prior to applying the static Newtoni-an law of gravitation, it must be veri�ed for movingbodies, but this is a prerogative of the experiment.

The theories of evolution of the Universe will remainthe hypotheses for ever, because none of assumptions(even on the isotropy and homogeneity) can be veri-�ed: \a moving train, which departed long ago, canbe catched up only at the other place and at the othertime." GRT assigns to itself the resolution of a series ofparadoxes (gravitational, photometric, etc.). However,the classical physics has also described the possibili-ties of resolution of similar paradoxes (for example, by


means of Charlier's structures, etc.). Apparently, theUniverse is not a spread medium, and we do not knowat all its structure as a whole to assert the possibilityof realization of conditions for similar paradoxes (moreprobably, the opposite situation is true). For example,the Olbers paradox can easily be understood on the ba-sis of the analogy with the ocean: the light is absorbed,scattered and re ected by portions, and the light sim-ply ceases to penetrate to a particular depth. Certainly,such \a depth" is huge for the rare�ed Universe. How-ever, the ashing stars represent rather compact objectsspaced at great distances from each other. As a result,only a �nite number of stars make a contribution intothe light intensity of the night sky.

The expanding of the Universe gives a red shift ac-cording to the Doppler e�ect irrespective of GRT. Be-sides, it should be taken into consideration, that eventhe elementary scattering will make contribution in-to the red shift and �lling of the so-called relic radi-ation: recall that the Compton e�ect gives waves with�0 > �0 . The shift of lines in the gravitational �eld hasbeen well predicted even by mechanistic models fromthe general energy considerations.

Now we pass to the following principal issue. Whetherpositive is the fact, that the distribution and motionof the matter cannot be speci�ed arbitrarily? Andwhether is it correct? Generally, this implies the incon-sistency of the theory, because there exist other forces,except gravitational ones, which are also capable totranspose the matter. From the practical viewpointthis means, that we should specify all distributionsin \the correct-for-GRT" manner even at the initialtime instant. In such a case we should refer t0 instantto \the time of creation," did we? And what prin-ciples should be unambiguously determinate for sucha choice? This requires more knowledge, than it isexpected from GRT. Open to question occurs to bethe possibility of point-like description and the theoryof disturbances, because the resulting values cannotbe arbitrary as well. The joining of a completely un-known equation of state implies arti�cial complicationof macro- and micro-levels by linkage and re ects thepossibility of arbitrary �ttings (for example, the tem-perature dependence is rejected). The possibility ofadding the cosmological constant into Einstein's equa-tions is an indirect recognition of ambiguity of GRTequations and of possible outrage. If everything canbe speci�ed to such an accuracy, then why cannot wespecify in arbitrary manner the initial distribution andthe motion of a matter?

Let us discuss one more principal point concerningthe relativity of all quantities in GRT. The laws, writtensimply as the equations, determine nothing by them-selves. The solution of any problem still requires theknowledge of speci�c things, such as the characteristicsof a body (mass, shape etc.), the initial and/or bound-ary conditions, the characteristics of forces (magnitude,

direction, points of application etc.). \The referencepoints" are actually speci�ed, with respect to whichthe subsequent changes of quantities (position, veloc-ity, acceleration etc.) are investigated. The principalrelativity of all quantities in GRT contradicts the ex-periments. The subsequent arti�cial attempt to deriveaccelerations (or rotations) with respect to the localgeodesic inertial Lorentzian system - this is simply the�tting to only workable and experimentally veri�ed co-ordinates of the absolute space (GRT does not containany similar things organically [7]).

The Mach principle of stipulation of an inert massand absolute nature of the acceleration due to the in u-ence of far stars is also doubtful, since it explains the in-trinsic properties of one body via the properties of otherbodies. Of course, the idea is elegant in itself. If ev-erything in the world is supposed to be interdependentand some ideal complete equation of state is believed toexist, then any property of bodies should be determinedby the in uence of the whole remaining Universe. How-ever, in such a case any particle should be consideredto be individual. This way is faulty for science, whichprogresses from smaller knowledge to greater, since \itis impossible to grasp the immense." Actually, if wetake into account the non-uniform distribution of mass(in compact objects) and di�erent values of attractionforces from close and far objects, then the complete\tugging" would be obtained instead of uniform rota-tion or uniform inertial motion of an object.

The Mach principle cannot be veri�ed in essence:both removal of all bodies from the Universe and tend-ing of the gravitation constant to zero are the abstrac-tions having nothing in common with the reality. How-ever, it is possible to estimate the in uence of \farstars" experimentally by considering the mass of theUniverse as mainly concentrated in compact objects.The force of attraction of a star having a mass of theorder of the Sun's mass (M � 2 �1030 kg), being at thedistance of 1 light year (� 9 � 1015 m), is equivalent tothe action of a load having a mass of only m0 � 25 g atthe distance of 1 meter. We shall make use, for a while,of the doubtful Big Bang theory and shall consider thetime for the Universe to be equal to � 2 � 1010 years.Even if the stars y away with light speed, we wouldhave the size of the Universe equal to � 2 � 1010 lightyears. We have deliberately increased all quantities;for example, the mass of the Universe and its density� � 1033=1054 � 10�21 g=cm3 . We take into accountnow, that, as the bodies move away from each otherat the two-fold distance, the force decreases four-fold,etc. Even if we suppose the mean distance betweenthe stars to be 1 light year, then at the distance of 1meter it is necessary to place the mass (we sum up to2 �1010) of M0 � 25(1+1=4+1=9+ � � �) = 25

P1=n2 �

25�2=6 < 50 g. In fact, coe�cient �2=6 expresses somee�ective increase of the density at the observation line.To simulate the action of \the whole Universe" we can

232 S.N. Arteha

1

R 2

R 3

1

2

r

R’2

R’3

Figure 2: The Mach principle and in uence of the Universe

take a thick metal sphere with outer radius of 1 meterand make its thickness varying in the direction to thecenter.

Let the width of a solid sphere be 0:6 meters, i.e.from the center up to 0:4 meters there is a niche, andfurther, up to 1 meter, - the metal. Then a cylindricalcolumn of radius � 0:35 cm will correspond to massM0 at density of � 8:3 g=cm3 . In reality, we shouldtake into account the in uence of stars in a cone, butnot only in a cylinder. Though we also have a sphericalmetal cone, nevertheless, we shall estimate the ordersof magnitudes. We shall break a cone into cylindricallayers, which arise as the new layers of stars are in-volved into consideration (Fig. 2). Each new layer willbe greater, than a preceding layer, by 6 stars. The dis-tances from the center to the nearest boundary of eachlayer of stars can be found from the similarity of trian-gles: Ri=1 = i=r . Then we have R0i =

pi2(1 + r2)=r .

Therefore, the correction to a mass (we sum up to2 � 1010 ) will be found as

m0(1+1

4+ � � �)

�1+Xi

6

R02i

�< M0

�1+6r2

Xi

1

i

��

M0

�1 + 6 � 10�5 log (2 � 1010)

��M0(1 + 0:02):

Thus, our construction is quite su�cient for taking intoaccount \the whole Universe." Certainly, if the Uni-verse is in�nite, then the obtained harmonic series willdiverge, and the construction will be inadequate. This,however, contradicts both GRT and the modern ideas.

Let now place the globules on a spring inside thesphere. To avoid the collateral e�ects, the air can bepumped out from the structure and, in addition, theglobules can be isolated from the sphere by a thin ves-sel. Now, if we spin up the sphere, then, accordingto the Mach principle, the centrifugal force should ap-pear, and the globules will move apart of each other.

In this case the centrifugal force must be the same, asthough the globules themselves would rotate. It seemsquite obvious, that this is impossible, since such an ef-fect would be noticed still long ago. Thus, we return toabsolute notions of acceleration, mass, space and timede�ned still by Newton. However, the described ex-periment could appear to be useful for determining thecorrections to the static Newton's law of gravitation.In this case the globules should have su�cient freedomto move and to rotate, since the direction of action ofcorrecting forces and moments of forces is unknown apriori.

The gravitational constant is not a mathematicalconstant at all, but it can undergo some variations [9].Therefore, this value can account corrections to New-ton's static law of gravitation (for example, these in- uences do not taken into consideration for the dis-placement of the perihelion of the Mercury). General-ly speaking, the theory of short range for gravitationcould be useful (but it can be not useful depending onthe gravitation transmission rate) for the �nite numberof cases only: for the rapid (v ! c) motion of massive(the same order) bodies close to each other. The authordoes not know such practical examples.

The GRT approach to gravitation is unique: to beshut in the lift (to take pleasure from the fall) and tobe not aware that the end (hurt oneself) will be aftera moment. Of course, the real state is quite di�erentone: we see always where and how we move relative tothe attractive centre (contrary to Taylor and Wheeler,it is the second \particle," together with the �rst \par-ticle" | with the observer). That is the reason thatthe pure geometric approach is a temporal zigzag forphysics (although it could ever be useful as a auxiliarytechnique). And two travelers from the parable [10]have need for \very little": for the wish to move fromthe equator just along meridians (on the spheric earthsurface), but the rest of �ve billion mans can not havesuch the wish. Contrary to traveler's wish, the wish \todo not attract to the Earth (or the Sun) and to y awayto space" is inadequate. The notion force (the force ofgravity in this case) re ects this fact. Geometry cannotanswer to the following questions: how many types ofinteractions exist in nature, why there exist they on-ly, why there exist local masses, charges, particles, whythe gravitational force is proportional just to r2 , whythere realize the speci�c values of physical constants innature, and many other questions. These problems arethe physical (experimental) prerogative.

3. Conclusions

The paper is devoted to the GRT criticism. A set ofstriking doubtful points from the GRT textbooks is em-phasized, beginning with general concepts of the covari-ance, baseline physical notions, and �nishing with more


speci�c ones. The proof of the geometry invariance ina rotating coordinate system is carried out in detail.The groundlessness and inconsistency of the principleof equivalence in GRT is discussed. The inconsistencyof the notion of time and its synchronization in GRTis demonstrated. The methods of time synchronizationand simultaneous measurement of lengths are indicatedfor the most interesting special cases. The invariance ofspace geometry is demonstrated and the role of bound-aries is also discussed in the paper. The doubtful pointsare emphasized both for the methods and for numer-ous corollaries of GRT. The inconsistency of the notionof \black holes," of Schwarzschild's solution and oth-er GRT corollaries are considered in detail. The Machprinciple and its possible veri�cation are also discussed.

The ultimate conclusion of the paper consists in thenecessity of returning to classical notions of space andtime and of constructing the gravitation theory on thisestablished basis.

References

[1] S.N. Arteha, \On the Basis for Special Relativity The-ory," to be published in Galilean Electrodynamics.

[2] S.N. Arteha, \On Frequency-Dependent Light Speed,"to be published in Galilean Electrodynamics.

[3] S.N. Arteha, \On Relativistic Kinematic Notions," tobe published in Galilean Electrodynamics.

[4] L.D. Landau and E.M. Lifshitz, \The classical Theoryof Fields," Nauka, Moscow, 1988 (in Russian).

[5] P.G. Bergmann, \Introduction to the Theory of Rel-ativity," Inostrannaya Literatura, Moscow, 1947 (inRussian).

[6] E. Schmutzer, \Relativit �a tstheorie - Aktuell," Mir,Moscow, 1981 (in Russian).

[7] V. Fock, \The Theory of Space, Time and Gravita-tion," Pergamon Press, London, 1959.

[8] A.A. Logunov, M.A. Mestvirishvili, \Relativistic Theo-ry of Gravitation," Nauka, Moscow, 1989 (in Russian).

[9] V.P. Ismailov, O.V. Karagios, A.G. Parkhanov, \TheInvestigation of variations of experimental data for thegravitational constant," Physical Thought of Russia1/2, 20{26 (1999).

[10] E.F. Taylor, J.A. Wheeler, \Spacetime Physics,"W.H. Freeman and Company, San Francisco, 1966.


ANOMALIES IN MOVEMENT OF \PIONEER 10/11"

AND THEIR EXPLANATION

N.A. Zhuck1

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

August 17, 2002

The author has o�ered the version of an explanation of anomalies of the Pioneer 10/11 motion on the basis of theUniverse gravitational viscosity.

Pioneer 10 was launched on 2 March 1972 and itfunctions till now.

Pioneer 10 distance from Sun: 80.68 AU Speed rel-ative to the Sun: 12.24 km/sec (27,380 mph) Distancefrom Earth: 12.21 billion kilometers (7.59 billion miles)Round-trip Light Time: 22 hours 38 minutes

Launched on 5 April 1973, Pioneer 11 followed itssister ship. Its mission ended on 30 September 1995,when the last transmission from the spacecraft was re-ceived.

Pioneer 10/11 have anomalies in the motion. A dis-cussion of this phenomenon appears in the 4 October1999 issue of Newsweek magazine. The mystery of thetiny unexplained acceleration towards the Sun in themotion of the Pioneer 10, Pioneer 11 and Ulysses space-craft remains unexplained.

A team of planetary scientists and physicists led byJohn Anderson has identi�ed a tiny unexplained accel-eration towards the Sun in the motion of the Pioneer10, Pioneer 11, and Ulysses spacecraft. The anoma-lous acceleration | about 10 billion times smaller thanthe acceleration we feel from Earth's gravitational pull(0:76�10�10 m/sec2 in report [1]) | was identi�ed afterdetailed analyses of radio data from the spacecraft.

A variety of possible causes were considered includ-ing: perturbations from the gravitational attraction ofplanets and smaller bodies in the Solar system; radi-ation pressure, the tiny transfer of momentum whenphotons impact the spacecraft; general relativity; in-teractions between the Solar wind and the spacecraft;possible corruption to the radio Doppler data; wobblesand other changes in Earth's rotation; outgassing orthermal radiation from the spacecraft; and the possiblein uence of non-ordinary or dark matter.

After exhausting the list of explanations deemedmost plausible, the researchers examined possible mod-i�cation to the force of gravity as explained by New-


ton's law with the Sun being the dominant gravitationalforce.

However in 1984 the author of this work has deducedthe new formula of a free motion of a material bodyinstead of the Newton's �rst law [2]

d2X

dt2+H

dX

dt= 0; (1)

where the label is entered

H =

r4�G�0

3; (2)

which corresponds to the Hubble constant, but has oth-er physical sense (here �0 is medial density of the Uni-verse; X is a coordinate). It now re ects a dissipationof energy at a motion of material bodies and at spreadof �elds. The Hubble constant is very small and equalapproximately 10�18 1/sec.

Medial density of a substance is equal approximate-ly 4 � 10�21 kg/m3 in region of Solar system (one starper 10 cubic kiloparsecs). Then the Hubble parameterwill be equal 1:1 � 10�15 1/sec. And the acceleration ofPioneer 10 equal (�1:3) � 10�11 m/sec2 for the presenttime. Earlier acceleration was more.

Thus, the gravitational viscosity is the most proba-ble reason of motion anomaly of the Pioneer 10/11. Atleast gravitational viscosity should be studied.

References

[1] N.I. Kolosnitsyn. \Relativistic orbit form and anoma-lies in \Pioneer 10/11" dynamics." Abstracts of 11-thInternational Conference \Theoretical and experimen-tal problems of General Relativity and gravitation,"2002, pp. 68-69.

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


AGAIN ON THE GUALA-VALVERDE HOMOPOLAR-INDUCTION

EXPERIMENTS

Ricardo Achilles1

Con uencia Tech University, Rosas y Soufal - P. Huincul Neuquen, ARG Q8318EFG

Received December 21, 2002

After independent repetition of the recently reported break-through experimentation on homopolar induction byGuala-Valverde et al [Apeiron, 8, 41 (2001)] some considerations are drawn on the torque-production mechanismapplicable to machines founded on that principle. These considerations are based on the \action-at-a-distance"Ampre-Weber-Assis rationale.

1. Introduction

The Guala-Valverde (G-V) and coworkers success insolving the old conundrum known as homopolar induc-tion rests upon the singularity introduced in an uniformmagnet [1], [2], [3], [4], [5] providing a local, short rangeB-�eld reversion. The most striking feature of the G-Vhomopolar-motor experiments occurs when the probeis located in the singularity: while the free-to-rotateprobe denotes the presence of forces in correspondencewith the �eld reversion observed in that region, the sta-tionary circuit-closing wire remains insensitive to themagnet singularity. It behaves as if there were no sin-gularity at all! This experimental fact enabled G-V tolocate the seat of electromotive and ponderomotive ac-tions in homopolar machines [1] con�rming besides thesymmetry of both, generator and motor con�gurations.The aforementioned, quiet a trivial fact for ordinary ux-varying machines, was a rather obscure issue foralmost two centuries in the homopolar devices' case.

Energy conversion by a machine is made possible bythe relative motion of two of its constitutive parts; inthe speci�c case of electrical machines these two partsare an active conductor -the probe or the closing wire inG-V's nomenclature- and a magnet (or a second activeconductor). Any electrical-circuit part anchored to themagnet will no longer play an active energy-conversionrole; it will be just a current-path closing means. Theremaining electrical circuit -with motion relative to themagnet enabled- takes over energy conversion (mechan-ical to electrical for a generator or vice versa for a mo-tor). Fig. 1 sketches a homopolar motor where a cen-tripetal direct current is applied to the probe attachedto the upward B-�eld face of a disk magnet. The maininteraction in this case can be split in two [1], [6]:


Figure 1: Torques on the homopolar-motor magnet andclosing wire

| Magnet-probe: The magnet exerts a counter-clockwise torque on the probe, the probe an equal butopposite torque on the magnet.

| Magnet-closing wire: The magnet exerts a clock-wise torque on the closing wire, the closing wire anequal but opposite torque on the magnet.

The probe attached to the magnet does not permitrelative motion and the action-reaction cancellationmechanism among both parts inhibits energy conver-sion. On the contrary, the closing wire -with electricalcontinuity with the probe attained via the mercurycollector rings- possesses relative motion with respectto the magnet enabling energy conversion. This lat-ter interaction is the main responsible for the observedmagnet-plus-probe rotation. Ironically, and againstthe customary absolutist argument of the magnet be-ing dragged by the probe [1], the magnet is the drag-

236 Ricardo Achilles

Figure 2: Ampre-law current elements

ging agent. The additional closing wire-probe (current-current) interaction was dismissed in the G-V analysisdue to its negligible e�ect in comparison to the de-scribed mechanism.

As an IEEE member, last months some special-ists came along asking me on the homopolar torque-production mechanism. I am intending to answer onthis issue here.

2. Ampre versus StandardElectrodynamics

Ampre force law [7], [8], draws the expression for themagnitude of the mechanical forces applied on two cur-rent elements Idl, I'dl' separated a distance r (see Fig.2) as:

d2F = �(�o=4�)(I � I0=r2)[(2(dl � dl0)��3(r � dl)(r � dl0)=r2]: (1)

This formulation supplies a quite suitable tool tobetter understand the homopolar phenomena: the d2Fforces obey Newton's third law being its direction coin-cidental with the one of the segment rde�ning the dis-tance between the current elements. Repulsion (attrac-tion) occurs for a positive (negative)d2F magnitude.

As it is well known, a magnet may be modeled byAmpre equivalent magnetizing currents [9], [10]. Inthe homopolar-motor uniform B-�eld case, the magnetcan be de�ned as a cylindrical azymuthal current shell.The equivalent current I' of such a cilindrical magnet isshown in Fig. 3, in conjunction with a centripetal con-duction current I circulating through the probe. A fewquantitative considerations based on equation (1) canbe applied to the above described con�guration to un-derstand the homopolar torque-production mechanism:the Ampre formulation dependence on (1/r2 ) de�nesthe magnetic-shell current elements located more close-ly to the probe as the ones producing the main inter-action. Let us consider the action of two such currentelements I'dl' and a probe conduction-current elementIdl (see Fig. 3): an attraction force d2F'1 (repulsionforce d2F'2 ) will appear on the magnet-shell elementdl' located above (below) the probe element dl. Suchforces will include, in the general case indicated in the

Figure 3: Magnetizing shell-probe Ampre interaction in theuniform �eld motor

�gure, radial and azymuthal components acting on thebulk of the magnet. These latter components are themain responsibles for the observed clockwise rotation.This dominant interaction can be eliminated simply byattaching the probe to the magnet. In such case, theonly interaction left is the counterclockwise torque ap-plied on the magnet by the closing-wire current.

Standard Electrodynamics (SE) considerations basedon the Laplace's expression dF= I(dlxB) applied to themagnetizing current elements fail to explain homopolar-devices torque production since -by vector productproperties- all the forces acting on the shell currentelements are radial to the magnet and, therefore, un-able to generate torque (It has to be kept in mind thatduring the last century the unrestricted equivalenceof the Ampre and SE formulations was con�rmed forclosed circuits [7]). Moreover, a closed circuit in thevicinity of an arbitrary current element will apply onit forces perpendicular to its length (a fact manifestlyobserved in the probe). In the G-V experiments theinteraction to look at is the one existing between a�nite current element (the probe or the closing wire)and a closed circuit (the B-�eld equivalent magnetiz-ing current). And here, according to SE, the closingwire is unable to produce any torque on the magnet:a fact quite in opposition to experience! Conversely,the interaction of the magnet with the mechanicallyattached probe- plus-closing-wire circuit leads to thesame outcome for either formulation: a null torque onboth, closed circuit and magnet [7], [11]. At last, it isalso interesting to have a look of the current interactiontaking place in the magnet's singularity shown in Fig.4. The currents interacting here are the centripetal

Again on the Guala-Valverge Homopolar-Induction Experiments 237

Figure 4: Magnetizing shell-probe Ampre interaction in theG-V dynamotor magnet singularity

conduction current through the probe and the equiv-alent magnetizing-shell current along the singularity'sedges. While the upper-edge magnetizing current re-pels the probe with elementary forces d2F1 , the loweredge attracts the probe with forces d2F2 resulting ahigh-magnitude clockwise torque on it.

3. Final Remarks

A conclusive statement on the superiority of the Ampreformulation for the analysis of the interaction beetweencurrent-carrying wires and uniform magnets has beenderived from the G-V experiments. The requirementof relative motion among both parts here, is in strictcorrespondence with the similar for generation action[10]. Conversely Grassmann SE -attributing motor ac-tion unilaterally to the probe wire even if attached tothe magnet- fails in recognize homopolar machines' fullsymmetry.

The Ampre-formulation inclusion in electromag-netism programs at both intermediate and graduatelevels seems a necessary outcome of this article.

This essay is ended with Maxwell's quote on theAmpre expression: \The whole theory . . . is summedup in a formula . . . which must always remainthe cardinal formula of electrodynamics". James ClerkMaxwell, A Treatise on Electricity and Magnetism.Dover (1954). [See also references 7 and 8].

\We are to admit no more causes of natural thingsthan such as are both true and su�cient to explain theirappearances." (Newton).

Acknowledgments: To Norpatagnica R&D fortheir helpful technical assistance. To Jorge Guala-Valverde who de�nitively �red my interest in Weber'sElectrodynamics and on the Ampre force. To PedroMazzoni for his mastery in experimental physics.

References

[1] J. Guala-Valverde & P. Mazzoni, Apeiron, 6, 202(1999).

[2] J. Guala-Valverde, P. Mazzoni, Spacetime & SubstanceJournal, 12, N 4, 785 (1999).

[3] J. Guala Valverde, P. Mazzoni & R. Achilles, AmericanJournal of Physics, 70, N 10, 1052 (2002).

[4] J. Guala Valverde, Physica Scripta. 66, 252, (2002).

[5] J. Guala-Valverde, Spacetime& Substance, 3, 94 (2002)

[6] J. Guala-Valverde, \In�nite Energy." To be published(Dec. 2002)

[7] A.K.T. Assis, \Weber's Electrodynamics." Kluwer,Dordrecht, 1994.

[8] A.K.T. Assis, \Relational Mechanics." Apeiron, Mon-treal, 1999.

[9] K.K.H. Panofsky and M. Phillips, \Classical Electricityand Magnetism." Addisson Wesley, New York, 1955.

[10] T.E. Phipps Jr. & J. Guala-Valverde, 21st CenturyScience & Technology, 11, 55 (1998).

[11] M. Bueno & A.K.T. Assis, \Inductance and Force Cal-culation in Electrical Circuits." Nova Science Publish-ers, Huntinghton, New York, 2001.


Spacetime &SubstanceContents of issues for 2002 year

Vol. 3 (2002), No. 1 (11)

Viktor Aleshinsky. ELECTRODYNAMICS: THE CONSISTENT FORMULAS OF INTERACTION FOR ACURRENT ELEMENTS, A MOVING CHARGES AND NEW EFFECTS (1).

Michel Bounias. ON SPACETIME DIFFERENTIAL ELEMENTS AND THE DISTRIBUTION OF BIO-HAMILTONIAN COMPONENTS (15).

P. A. Varenik and Yu. P. Varenik. THE NEW VIEW ON THE NATURE OF BODYS INERTIA ANDLAWS OF NEWTONIAN DYNAMICS (20).

V.V. Dvoeglazov. GENERALIZED NEUTRINO EQUATIONS BY THE SAKURAI-GERSTEN METHOD](28).

Miroslav Sukenik and Jozef Sima. THE HYDROGEN ATOM | A COMMON POINT OF PARTICLEPHYSICS, COSMOLOGY AND CHEMISTRY (31).

Miroslav Sukenik and Jozef Sima. NEUTRON STAR PROPERTIES VIEVED BY THE ENU MODEL (35).

L.C. Garcia de Andrade. ON STRING COSMOLOGY AND DE SITTER INFLATION WITH MASSLESSDILATONS AND DYNAMICAL TORSION (38).

C.A. de Souza Lima Jr. and L.C. Garcia de Andrade. GROWTHAND DECAYOF INGOMOGENEITIESIN NEWTONIAN COSMOLOGY: SPIN EFFECTS (39).

L.C. Garcia de Andrade and C. Sivaram. TORSIONGRAVITATIONAHARONOV-BOHM EFFECT (42).

L.C. Garcia de Andrade. TORSION GRAVITY EFFECTS ON CHARGED-PARTICLE AND NEUTRONINTERFEROMETERS (45).

Rasulkhozha S. Shara�ddinov. ON THE COMPOUND STRUCTURES OF THE NEUTRINO MASS ANDCHARGE (47).

Vol. 3 (2002), No. 2 (12)

L.P. Fominskiy. TO CONCEPT OF AN INTERVAL OR BASIC MISTAKE OF THE THEORY OF RELA-TIVITY (49).

N.A. Zhuck. THE NEW STATIONARYMODEL OF THE UNIVERSE. COMPARISON TO THE FACTS (55).

N.A. Zhuck. THE EARTH AS THE GRAVITATIONAL-WAVE RESONATOR (67).

L.V. Grunskaya, V.V. Isakevitch, V.A. E�mov, I.N. Gavrilov, M.S. Gerasimov. INTERCOMMUNICATIONOF ELECTROMAGNETISM OF THE SURFACE LOVER LAYERWITH GEOPHYSICAL AND ASTRO-PHYSICAL PROCESSIS (69).

Anirudh Pradhan and Hare Ram Pandey. PLANE SYMMETRIC COSMOLOGICAL MODELS IN THEPRESENCE OF ZERO-MASS SCALAR FIELDS (76).

Spacetime &Substance, Vol. 3, No. 5 (15), 2002 239

V.L. Kalashnikov. CONSTRAINTS ON THE COSMOLOGICAL PARAMETERS IN THE RELATIVISTICTHEORY OF GRAVITATION (81).

Valeri V. Dvoeglazov. SOME MATHEMATICAL BASES FOR NON-COMMYTATIVE FIELD THEORIES(84).

Rasulkhozha S. Shara�ddinov. ON THE ANOMALOUS STRUCTURES OF THE VECTOR LEPTONICCURRENTS (86).

Sutapa Ghosh and Somenath Chakrabarty. CAN THERE BE � -EQUILIBRATED QUARK MATTER ATTHE CORE OF A COMPACT NEWBORN NEWTRON STAR WITH MODERATELY STRONG MAG-NETIC FIELD? (88).

Jorge Guala-Valverde. FEYNMAN LECTURES, A-FIELD AND RELATIVITY IN ROTATIONS (94).

Vol. 3 (2002), No. 3 (13)

Scott M. Hitchcock. THE CREATION OF TIME FROM SUBSTANCE AND SPACE (97).

Vasile Mioc. SYMMETRIES OF THE GRAVITATIONAL N-BODY PROBLEM (104).

Alex M. Chepick. THE CALCULATION OF THE INDISPENSABLE ACCURACY OF THE MEASURINGOF AN EM-WAVE'S ENERGY (108).

Valery P. Dmitriyev. GRAVITATION AND ELECTROMAGNETISM (114).

Miroslav Sukenik and Jozef Sima. ELECTROMAGNETIC INFLUENCE ON GRAVITATIONAL MASS {THEORY, EXPERIMENTS AND MECHANISM OF THE SOLAR CORONA HEATING (118).

A.M. Chepick. SUPREMUM OF THE INTERACTION SPEED OF THE MATTER (122).

Valeri V. Dvoeglazov. SOME MATHEMATICAL BASES FOR NON-COMMYTATIVE FIELD THEORIES(125).

Afsar Abbas. TO QUANTIZE OR NOT TO QUANTIZE GRAVITY? (127).

Angelo Loinger. RELATIVISTIC MOTIONS (129).

Antonio Alfonso-Faus. QUANTUM GRAVITY AND GENERAL RELATIVITY CONSISTENT WITH A DE-CREASING SPEED OF LIGHT AND MACH'S PRINCIPLE (130).

Rasulkhozha S. Shara�ddinov. THE UNITED THEORY OF THE TWO FIELDS OF THE ELECTRIC ANDMAGNETIC NATURE (132).

Rasulkhozha S. Shara�ddinov. ON THE TYPE OF THE SPIN POLARIZATION DEPENDENCE OF THENEUTRINO MASS AND CHARGE (134).

Jorge Guala-Valverde. ON THE ELECTRODYNAMICS OF SPINNING MAGNETS (140).

Vol. 3 (2002), No. 4 (14)

Angelo Loinger. GRAVITY AND MOTION (145).

Savita Gehlaut, A. Mukherjee, S. Mahajan and D. Lohiya. A \FREELY COASTING" UNIVERSE (152).

Fangpei Chen. THE RESTUDY ON THE DEBATE BETWEEN EINSTEIN AND LEVI-CIVITA AND THEEXPERIMENTAL TESTS (161).

240 Contents of issues for 2002 year

A. Pradhan and O.P. Pandeyc. CONFORMALLY FLAT SPHERICALLY SYMMETRIC COSMOLOGI-CAL MODELS-REVISITED (169).

R. Ru�ni, M. Lattanzi, C. Sigismondi and G. Vereshchagin. CHEMICAL POTENTIAL OF MASSIVENEUTRINOS IN AN EXPANDING UNIVERSE (174).

D.L. Khokhlov. SPACE-TIME IN THE CLASSICAL ELECTRODYNAMICS FROM THE VIEWPOINT OFQUANTUM MECHANICS (179).

A.M. Chepick. MEASUREMENTS WILL SHOW DECREASING OF THE HUBBLE CONSTANT (181).

A.M. Chepick. WHY THE HUBBLE PARAMETER GROWS UP? (183).

Fabio R. Fernandez. MORE ON FEYNMAN LECTURES BY J. GUALA-VALVERDE (184).

Jorge Guala-Valverde, Pedro Mazzoni and Cristina N. Gagliardo. WHYHOMOPOLAR DEVICES CAN-NOT BE ADDITIVE? (186).

DISCUSSION (188).

2ND GRAVITATION CONFERENCE IN KHARKIV (190).

Vol. 3 (2002), No. 5 (15)

Troitskij, V.I. Aleshin. EXPERIMENTAL EVIDENCE OF THE MICROWAVE BACKGROUND RADIA-TION FORMATION THROUGH THE THERMAL RADIATION OF METAGALAXY STARS (193).

Yu.M. Galaev. THE MEASURING OF ETHER-DRIFT VELOCITY AND KINEMATIC ETHER VISCOSITYWITHIN OPTICAL WAVES BAND (207).

S.N. Arteha. ON THE BASIS FOR GENERAL RELATIVITY THEORY (225).

N.A. Zhuck. ANOMALIES IN MOVEMENT OF \PIONEER 10/11" AND THEIR EXPLANATION (234).

Ricardo Achilles. AGAIN ON THE GUALA-VALVERDE HOMOPOLAR-INDUCTION EXPERIMENTS(235).

Spacetime &Substance. Contents of issues for 2002 year (238).

Spacetime &SubstanceInternational Physical Journal

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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.

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Spacetime &Substance Volume 3, No. 5 (15), 2002

CONTENTS

V.S. Troitskij, V.I. Aleshin. EXPERIMENTAL EVIDENCE OF THE MICROWAVEBACKGROUND RADIATION FORMATION THROUGH THE THERMAL RADIATIONOF METAGALAXY STARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Yu.M. Galaev. THE MEASURING OF ETHER-DRIFT VELOCITY AND KINEMATICETHER VISCOSITY WITHIN OPTICAL WAVES BAND . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

S.N. Arteha. ON THE BASIS FOR GENERAL RELATIVITY THEORY . . . . . . . . . . . . . 225

N.A. Zhuck. ANOMALIES IN MOVEMENT OF \PIONEER 10/11" AND THEIR EX-PLANATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

Ricardo Achilles. AGAIN ON THE GUALA-VALVERDE HOMOPOLAR-INDUCTIONEXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

Spacetime &Substance. Contents of issues for 2002 year . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

ternational In ysical Ph Journal - Orgone · U K R A I N E ISSN 1726-4499 Spacetime & Substance...

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