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ISSN 1726-4499
Spacetime & Substance International Physical Journal
Volume 5, No. 2 (22), 2004 c 2004 Research and Technological Institute of Transcription, Translation and Replication JSC
Spacetime & Substance International Physical Journal
ISSN 1726-4499
Certicate of the series AB, No. 4858, issued by the State Committee for Information Policy, TV and Broadcasting of Ukraine (February 12, 2001). The Journal is published by Research and Technological Institute of Transcription, Translation and Replication, JSC(Kharkiv, Ukraine). It is a discussion journal on problems of theoretical and experimental physics in the eld of research of space, t||||imdtamehep,asepsctlutrhihibcepaesmtottiairaoointnenicscoeoacfflaosnmtmehdtobe-uodiinnpretiilsenessragaaifnmcsoptdreiaoddpcneehass,it.cltortTiishmpohetpeeir,hoeJgniacorlauaaizlvrnanbidttaai/aolsoteniprsou,onebfxwlapfihunsliahndcnedhosaa:tttmhoioueenrncsshtaiontlfhtppeehrrydaoscepitsceicarortlniipeestxs(ipoionenfrctilomuhfdeeainUnptgnshitayvhnseeidrcsaEetlhianrenesfatdoelriimtntyh'is;ccorSomRcionasgmndroesGs;uRlt)s;; | discussion of published materials, in particular, those questions, which still have not a correct explanation. EngTlihshe.vTolhuemeequoifvoanleenitssvueersiison4s8: ppaagpeesr. aFnodrmelaetctirsoAni4c.(*T.hTeEpXe,ri*o.dPiSci,t*y.PisD5Fi)s.sues per one year. The language is
Editorial Board:
N.A. Zhuck (Kharkiv, Ukraine) P. Flin (Krakow, Poland)
V.I. Noskov (Moscow, Russia)
L.P. Fominsky (Cherkasy, Ukraine) Yu.M. Galaev (Kharkiv, Ukraine)
J. Quiroga (Pereira, Colombia) V.L. Rvachev (Kharkiv, Ukraine)
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M.M.Abdildin (Almaty, Kazakhstan) N.D. Kolpakov (Kharkiv, Ukraine) (Kharkiv, Ukraine)
L.Ya. Arifov (Simferopol, Ukraine) A. Loinger (Milan, Italy)
V. Skalsky (Trnava, Slovakia)
Yu.A. Bogdanov (Kharkiv, Ukraine) I.Yu. Miklyaev (Kharkiv, Ukraine) V.I. Skubaev (Cherkasy, Ukraine)
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c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 49{52 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
N Center for Relativity and Astrophysics, 185 Box, 194358, Sanct-Petersburg Russia General Physics Institute of the Russian Academy of Sciences, 38 Vavilova str., Moscow, 119991, Russia Received August 31, 2004
In Klein geometric model of space the mass is manifestation of the quantized charges oscillations in additional compactied dimension. We analyze model in which common in four-dimensional space-time for mass and electric charge of the particle trajectory is disintegrated in ve dimensions on movement of the mass along null geodesic line and trajectory of the charge corresponding to the time-like interval in 5D volume. We nd relation between ve-velocity vector of electric charge and mass. This scheme is regarded to have concern with many worlds theory. Considered approach is applied to the model of rotating space having four-dimensional spherical symmetry. One proposed appearance additional force in included 4D space-time, which may be explanation of the Pioneer-eect. We analyze also possible part of this force in conservation of the substance in Galaxy area.
Several theories, being studied ve-dimensional space-time, are founded on dierent on physical principles. Generalization of the special theory of relativity for 5D ehxatsenbdeeend psproapceosGed(Ta;nX~d;dSe)vewloitphedthienmweotrrkics([+1-;8-],.-B, -u,i-lt) model of extended space (ESM) allows integration of the electromagnetic and gravitational interactions. The peculiarity of ESM is its studying of the particle trajectory in 5D basing on analogy between the light movement in curved space in general relativity and its mmoovreemtheannt iunnmityed[i2u,m3,6w].itIhnrEefSrMactmionascsooeftchieenptabrteiicnlge isitsnpraactnochsemifsopGrsom(pnTaeec;dneX~tint;ohSfee)ath.ceheleWcotvtirtheih-cev,rce.hgcrataonvrgietesyneoarfngdyco-iosmcradpliaunrlastee-emlfdraassmsairenes As the 5-th additional coordinate in ESM is used quantity, which already exists in the (1+3)-dimensional Mcdtin,inawkthoeswersxek1ic;sxpi2sa;lcxieg3h;Mxt3v(,Teln;oaXc~mit)ye,,lywt,iitinhsttetirimmvaeel,caSono:drdsipnaactee cxo0o=r-
S2 = (x0)2 (x1)2 (x2)2 (x3)2:
tranTshfoirsmqautiaonntsitiyn itshecMonisnekrovwedskiatspaccoemMmo(nT;LX~o)rebnutzt varies at turns in the extended space G(T; X~ ; S). Thus, Minkowski space M(T; X~ ) is a cone in extended space G(T; X~ ; S). In 5D gravity theory, begun by Nordstrom [9] and Kaluza [10], proposed by Klein [11] approach to the
1E-mail: [email protected] 2E-mail: [email protected]
p[i1na2r5-t1Dic5l]esrpmeaqcouevi.eremsOenintets aetnnrasaujleyrcestisosraeyxpatamortibniceelden,uhflaolvrgineexogadnmeospincl-ezl,einrinoe
time-like interval electromagnetism
0 = G~ij(xm)dximdxjm;
where tensor
xoimf 5aDrespmaacses,
cwohoricdhiniastefus nacntdionG~ iojf(xtmhe)seis cmooertdriic-
nates. On the contrary, electric charge has trajectory
with line element
ds2e = G~ij(x)dxidxj;
where xi are electric charge coordinates. Thus, world line of the particle mass in 5D inter- sects corresponding world lines of electric charges and, conversely, trajectory of the electric charge is a set of the points appertained to trajectories of corresponding masses. This approach leads us to proposed by Everett
W.B. Belayev and D.Yu. Tsipenyuk
[21-23] conception of many worlds founded on quantum theory. Let us touch relation of present scheme to anthropic principle. Our perception of environment arises by means of electro-magnetism and we can not feel gravity direct. This may be considered as account for assumption that to be exact mass, not electric charge moves along null pass in 5D. In this case we can hold that 5D space model with non-zero rest mass of the particle and appropriate time-like interval describes electro-magnetic \trace" of the masses, which appertain consecutively the world line of corresponding electric charges combination. Light velocity in extra dimension in coordinate frame of charge or system of charges being its source is assumed to be null. dofximtCh=eodmsepvfeoo-nvremenlotascitovyfe-vmveecactstosorr.voefWlocichtiahtyrgredsetunfiooutcerodcrroeamssppoounnimdeinn=tgs tdoeninceteorvfaml (a3s)s eaqnudalcihtiaersgeuimco=orduiinpatreosviidne 4loDc.alDcioviindceidEq. (2) on ds2e we obtain 0 = G~ijuiuj + (G~i4ui+ +G~4iui)ujm + G~44(u4m)2; i; j 6= 4: (4)
willAbtethis point the mass velocity along fth coordinate
u4m = (G~i42G+~4G4~4i)ui +
G~4i)2ui2 2G~44
4G~44G~ijuiuj ;
wMhicneorkneofworsmk=i stpoamc1e,awtite;ejrhaa6=vned4a.ntiT-mheatoteprp.osFitoer
values of extended
u4m = p1 + u42:
Let us apply considered conception to analysis of metric example of 5D space with such basis vectors that the fth of them is not orthogonal to others, which are basis of included 4D space. The cosmological model with movement of the matter along fth coordinate based oneself on metric conforming to this property has been studied in [20]. We analyze space-time, including four-dimensional spherical space, with coordinates xi = (ct; a; ; '; ) to be rendered to orthogonal frame by transformation
0 = ct;
1 = a sin sin cos ';
2 = a sin sin sin '; 3 = a sin cos ; (7)
4 = a cos :
is taTkheins isnpafcoermis assumed to be rotating and the metric
ds2 = c2[1 a2B(a)2]dt2 da2
a2[2cB(a)dtd+sin2 (d2+sin2 d'2)+d2];(8)
where B(a) is dependent on a coecient. In accordtoanthcee wmiothvecmonensitdoefrepdaratpicplreo'sacehlecwtirtoh-mdasg>ne0ticcotnrafocrem. s In [20] the geodesic line equations was written in form
d ds
1 2
@G~mj @xi
onfiotnFhaeolsretmyepqeeutra(itcui1o(n8=)s wuze2irt=ohthcuo,3m=rosv0ti)nagynidceolfdoorudritnhatceosmopf oconnenvtes-
d ds
a2Bu4] = 0;
@B @a

@B @a

d ds
by mSoelturticio(n8o)fctohnidsistyiosntem must be compatible with set
u02 a2(u4 + Bu0)2 = 1:
Such solution will be
u0 = ; u4 = B(a);
wcohmerpeonenttakoefsmvaaslusesve1-vaenlodcity1(.5)Ciosrfroelslpoownindgin:g fth

We notice that this equation with other four compmoansesnbtsutofituiims odnolyesvneolotciptuytonfumllagsesoidneseivcesryof ppoairntticolef charge geodesics. Considered coordinate frame is transformed to coobrydeinxaptreesssxioin=s (ct; r; ; '; y) having only 3D symmetry
r = a cos ;
y = a sin :
ticleWgeeodnedsiaccmceolevreamtieonnt sde2tr=bdysE2 pfatrhcoordinate is = 0. In this case we obtain y = 0 and
dwrr=itdtsen=a0s. The fth component of the ve-velocity is
1 +
dy ds
dr ds

This equation yields
dy ds

as Equation of the system (9) with i = 1 is rewritten
d2a ds2
After some transformations we obtain
d2r ds2
cludTehdu4sD, rsoptaactieo.nTihnis5fDorcgeiviessinavdadriitaibolneawl iftohrce in in-
B(a) = Ka 1=2;
where K is constant. One may be considered as ex-
planation of additional acceleration of the Pioneer 10
aonp we
=the8:E5ar1t0h [82c5m-2=7s]2. tAowssaurmdsedtointtheervraelcetiovibneg obtain value of the constant which is K
antenna d=s =0:9c7dt
10 13cm 1=2.
This additional acceleration satises to the con-
sistrvaeinlotciatpyRo&f tvhs2ews,owlahrewreinRd i[s28G].alIatxyfolrlaodwiussfraonmd tvhsiws
that if Pioneer-eect spreads on whole Galaxy area, it
is conducive to conservation of the matter within the
bounds of Galaxy belt.
References [1] DsIntc.sYhtieutn.uitTyeasi(ppRoeunsFysuiizakin,keVA(.cBAaud. lelAmetnyidnroeofefvSL,ceiKebnercadetestv)k)ieP6hS,yos2oi3cb{s34, (2000); arXiv: gr-qc/0106093. [2] Ddhot.tvYpau:n/.o/zhTvusrinRpaeoln.sayspiuiek,.,rel6a0rVn, ..rAu(.1/9a9rt9Ai)cnleds(r/ien1e9v9,R9/u0ss6Iis0as.nple)d-;f . [3] Dgpyh.,YysuiV.cos/lT.02s7i0p,3e0nN1y7ou..4k,(28G),ra3v3i6ta{t3io3n8, (a2n0d01)C;osamrXoliov-: [4] D(B.Yulule.tTinsipoefnyLuekb,edKervattPkhieysSiocosbsItncshteitnuityea p(Ro uFsisziiakne Academy of Sciences)) 7, 39{49, (2001); arXiv: physics/0107007.
[5] DsI(n2tc.0sYht0ieu2tn.u)i;tTyeaasr(iXpRpeoiuvns:yFsuipiazkhni,yksAeVi(ccB.saA/ud0.le3lmAe0t2nyin0do0rfoe6efS.vcL,ieenKbceredaset)tv)ki6eP,hS3yo{so1icb5s-,
[6] D8ht1.tY,pu:/./zhuT9rs0ni7pa{el.9na1yp6ue,k.r,elarnI.s(rs2ul0/e0da1ort)vi(acinnleos/20v0R1/usRsioasns)ii; 081.pdf.
[7] D.Yu. Tsipenyuk, V.A. Andreev, \ElectrodynamiMcsoscinow,E(x1t9e9n9d)e(din RSpuascsiea,"n).preprint IOFAN 9,
[8] D.Yu. Tsipenyuk, V.A. Andreev, \Gravitational eMoescctoswi,n(2E00x1t)e(nidneRduSsspiaacne),." preprint IOFAN 4,
G. Nordstrom, German).
[10] TK.1K, 9a6lu6z(a1,9S2i1tz).(PinreGuesrsm. Aanka).d. Wiss. Phys. Math.
[11] O. Klein Z. Phys. 37, 895 (1926).
[12] J. Van Dongen, arXiv: gr-qc/0009087.
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[14] W.B. Belayev, \Extra force in Kaluza-Klein gravimUtykorlaothignyeeo,aryJn,ud"neRIn2ev3lai-tt2ei7vd,is2tt0iac0l3kA);saattrroX\piGhvy:rasgivcris-tq"act/(ioK0n3h,0a8rC0k7oiv6s-,.
[15] Piv.:S.gWr-qecs/so0n3,02G0e9n2.. Rel. Grav. 35, 307 (2001); arX-
[16] J(1.M99.7O);vaerrXduivin:,gPr.-Sq.c/W9e8s0s5o0n1,8P.hus. Rept., 283, 303
[17] Ja.rXPiovn:cger-dqec/L0e1o1n0,0P63h.ys. Lett. B 523, 311 (2001);
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F. Dahia, E.M. Monte, Lett. A 25, 1173, (2003);
Car.XRivo:mgerr-oq,c/M03o0d3. 0P4h4y. s.
[20] W(20.B01.);BaerlXayivev: ,grS-qpca/c0ti1m10e09a9n.d Substance 7, 63
[21] B.S. DeWitt, R. N. Graham, \The many-worlds INtno.tneGrUprnraeihvtaaemrtsioi,tnyPrPoinfrecQsestuo(an1n9tS7ue3mr)i.esMienchPahnyicssic,"s, ePdrsi.ncRe-.
[22] FTve.irJms.ietT,y"ipPeldreesrs,Rsin.(1P\9eQ8n6ur)oa.snetuamndCCo.nIcsehpatms ,oOf xSfpoarcdeUannid-
52 [23] DRo. uBtolehdmge, BPr.Je.ssH, Lileoyn,d\oTn,he19U93n.divided Universe," [24] Ggsiya."Cn.CtMrhaacnpVsmliatattiinoe,nan:\GdGeH.nCae.lrfaMLl tRadce.-l,VaLtitiovtnii,tdyo\nGa, tivity and Cosmology," IIL, Moskow, 1961.) [25] J.D. Anderson, P.A. Laing, E.L. Lau, A.S. Liu, M28.5M8.(1N9i9e8to);, aSr.XGi.vT: ugrru-qshc/e9v8,0P8h0y8s1.. Rev. Lett. 81, [26] SEann.e.GLeorm.. 1La0Taloauuunr,sud,Ash1w.S1eev,.a",kLX,iuXJlo,.XDnMgI.V-.rM-aAtnh.ngdNReeiereanstcooccno,en,l\etrTraePhts.ieAodn.aepMopLfaoaPrrieinionognt-, Mtgarl-eqeGcti/rn9ag9v0iot3yn021G49r.9a9v,itLaetsioAnarlcsW, Savavesoia,nFdraEnxcpe;erairmXeinv-: [27] J.D. Anderson, P.A. Laing, E.L. Lau, A.S. Liu, M08.2M00.4N(i2e0t0o2,);Sa.GrX. iTv:urgurs-qhce/v0,1P04h0y6s4. .Rev. D 65, [28] K. Trencevski, unpublished data, 2004.
W.B. Belayev and D.Yu. Tsipenyuk
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 57{60 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
Dipartimento di Fisica, Universita di Milano, Via Celoria, 16 - 20133 Milano, Italy
Received July 28, 2004
The notion of gravitational wave (GW) came forth originally as a by-product of the linear approximation of general relativity (GR). Now, it can be proved that this approximation is quite inadequate to a proper study of the hypothetic GW's. The signicant role of the approximations beyond the linear stage is emphasized.
otsauftbGi1sotR.nraaAlt(epsh[e1yiltd]s,isic[)s2a]hl.wlayIes,tlltMrhekseinneomakwpobwnpl,ersosktxihtihesmeplaaeitnc.imeeotan.irmMfoeaarpaxpwswreoieatxlslkimt(hgaerxtoaeirvdoyin)-, and is only Lorentz invariant. nwahtieWcsh,iictthasnreenbseeprergecydttuteconesdtorratonbsezfceoorrommteahstriaoounfagslhsoefa(gspeusnieteuardbaolle)cctohe-noasrnodgrie-, of reference system. A celebrated by-product of the linearized version of GinR19i4s4thWeenylot[3io]npooifntgerdavoituatttiohnaat,l rwigaovreou[1s]l,y[s2p].eaNkionwg,, tfohrecegroanvitmataitotnera,l i.eel.diosfath\eploiwneearlreizssedshvaerdsoiwon".exIenrdtseendo, a basic result of the Einstein-Infeld-Homann method [4] tells us that, as Weyl [3] wrote, \the gravitational force arises only when one continues the approximation beyond the linear stage." Even in the modern literature this fact is generally overlooked and, quite uncritically, the action on matter of a gravitational wave { e.g. of a plane wave { is formally computed. In conclusion,the linear approximation of GR { which is the favourite relativistic doctrine of the GW htruenattemrsen{t iosfctohme pqlueetsetlyioninoafdetqhueaGteWto' approximate beyOonndththeeotlhineerahrasntda,gief w([n4t]inaunedt[h5e])a,pwperoxnimdatthioant tspcshethrrseooosviyrceaaeesddpoithbafhyyttasihotciecnoatnrhtleveefrereenmGraielesWnintocyt'efsc[tfo6har]-are,oemr[g7dero]ia,.nnvila.yiett.eaatttihrpoaarnnotasdltfuhoceretmyldoadfctoaiaonnnosbstp:eeptcdhoieasis--l In the recent literature the above crucial role of the co-ordinate system is ignored. E.g., Itoh and Futamase have published a learned study on the third post-Newtonian equation of motion for relativistic comptthhaeicsthreabsrienmaarrocihnesi[c7[]7:c]o,\-Oo[r8nd]e;inpatrhtoeemirciosnrinedsgiutislotonui.rsceMdoeorftiigvvreaadtvioiutnantdfieoorr- 1E-mail: [email protected]
nal waves for those detectors [i.e. GEO600, LIGO,
TAMA300] is a relativistic compact binary system in
an inspiraling phase. The detectability and quality of
measurements of astrophysical information of such gra-
vitational wave sources rely on the accuracy of our theo-
retical knowledge about the waveforms. A high order,
say, third- or fourth-order, post-Newtonian equation
of motion for an inspiraling compact binary is one of
the necessary ingredients to construct and study such
waveforms [: : :]." Itoh writes (see the abstract of [8]): \Our resulting equation of motion admits a conserved
energy (neglecting the 2.5 PN radiation reaction eect),
is Lorentz invariant, and is unambiguous [: : :]."
These authors do not suspect that the radiation
taersmuistaabrlee cfhraamngeedoefpceon-doerndti,naatnedsycsatnemb.e Fduerstthroeyr,edthbeyy
are unaware that { as it is easy to prove { the motions of
point masses interacting only gravitationally { as, e.g.,
tohf ethtewosoclaormspyastcetmsta{rshaopfpseonmaelobnignagreieosdeorsitchelinbeosd[i6e]s,
apnodssicbolnes.equently an emission of GW's is obviously im-
More radically, nism" exists in GR
iftorcatnhebgeenperroavteidonthoaf tGnWo's\m[6]e.cha-
recently, through a kind letter of have known the existence of the
Prof. A. beautiful
memoir by Weyl [3].
Since it seems that the astrophysical community is
nporotdauwcaerienoafnWAePylP'sErNesDulItsX, ,Iatthtinhke evnedryofustehfeulprteosernet-
p2ouaoprfetrWh,eetmyhlee'.s\mInetmroodiur,ctwiohnichanadreSupmarmticaurlya"rlaynrdelseevcatns.t t1o,
in 1I99a9vaIilpumbylissehlfedofatvheirsyosphpoortrtNunoitteyefnotritalend a\pDoeldougcy-:
tion of the law of motion of the charges from Maxwell
equations" [9]. Now, my result is contained in Weyl's
treatment of Maxwell theory, see sect. 2. of [3]. Weyl
wrote that this theorem was \well known". Yes, but
Angelo Loinger
only to the Blessed Few! Gse.arMAchcokropnfuoIrtwgoohl,eadwnghdmoFehunattsa.mcaaIlsleeadm[7m],vy[e8r]ay.ttgenrattioenfultotothPe rroef-.
[8] Y. Itoh and T. Futamase, Phys. Rev. D, 68 (2003) 121501(R). [9] Y. Itoh, arXiv:gr-qc/0310029 v2 (12 February 2004). [10] A. Loinger, Nuovo Cimento A, 112 (1999) 407.
\Nil sapientiae odiosius acumine nimio". Seneca
References [1] A. Einstein, Berl. Ber., (1916) 688. [2] A. Einstein, Berl. Ber., (1918) 154. [3] H. Weyl, Amer. J. Math., 66 (1944) 591. [4] L. Infeld and J. Plebanski, Motion and relativity (Pergamon Press, Oxford, etc) 1960, see in particular Chapt. VI. [5] A. Scheidegger, Revs. Modern Physics, 25 (1953) 451. [6] For many proofs of the phantasmatic nature of GW's, see A. Loinger, arXiv:physics/0312149 v3 (11 February 2004), and the literature quoted there sub [6], in par- ticular: A. Loinger, Spacetime & Substance, 3 (2002) 129 and 3 (2002) 145; Idem, On Black Holes and Gra- vitational Waves, (La Goliardica Pavese, Pavia) 2002, Part II. See also: Idem, arXiv: gr-qc, astro-ph, physics (1998-2003). As it is known, the rst theoretical proof of the physicalnon-existence of the GW's wa sgiven by T. LeviCivita in 1017; see his fundamental memoir in Rend. Lincei, 26 (1917) 381; an English version in arX- iv:physics/9906004 (June 2nd, 1999). [7] As it is well known, the astrophysical community perseveres in the chase of Nothing, see e.g. the report on INTERNET (13 January 2004) by Szabolcs Marka, for the LIGO scientic collaboration, entitled \Search for the gravity wave signature of GRB030329/SN2003dh". Its abstract is as follows: \One of the major goals of gravitational wave astronomy is to explore the astrophysics of phenomena that are already observed in the particle/electromagnetic bands. Among potentially interesting sources for such collaboration are gravitational waves searches in coincidence with Gamma Ray Bursts. On March 29th, 2003, one of the brightest ever Gamma Ray Burst was detected and observed in great detail by the broader astronomical community. The uniqueness of this event prompted our search as we had the two LIGO Hanford detectors in coincident lock at the time. We will report on the GRB030329 prompted search for gravitational waves, which relies on our sensitive multi-detector data analysis pipeline specically developed and tuned for astrophysically triggered searches. WE DID NOT OBSERVE A GRAVITY WAVE BURST, WHICH CAN BE ASSOCIATED WITH GRB030329 [Capital letters by A.L.]. However, the search provided us with an encouraging upper limit on the associated gravity wave strain at the Hanford detectors."
Introduction and Summary. G.D. Birkho's at-
tempt to establish a linear eld theory of gravitation within
the frame of special relativity2 makes it desirable to probe
the potentialities and limitations of such a theory in more
general terms. In thus continuing a discussion begun at an-
other place3 I nd that the dierential operators at one's dis-
posal form a 5 dimensional linear manifold. But the require-
ment that the eld equations imply the law of conservation olifmeintetrhgeysean1d5mpoomsseinbtiulimtiesintoth1e s2im, wplheicfho,[email protected][email protected], xrekd=uc0e
to two cases, a The regular case
regular one (L) and a singular one (L) is nothing but Einstein's theory
of weak elds. Resembling very closely Maxwell's theory
of the electromagnetic eld, it satises a principle of gauge
invariance involving 4 arbitrary functions, and although its
gravitational eld exerts no force on matter, it is well suited
to illustrate the role of energy and momentum, charge and
mass in the interplay between matter and eld. It might
also help, though this is much more problematic, in point-
ing the way to a more satisfactory unication of gravitation
and electricity than we at present possess. Birkho follows the opposite way: by avoiding rather than adopting the 12
special operators mentioned above, his \dualistic" theory
(B) destroys the bond between mechanical and eld equa-
tions, which is such a decisive feature in Einstein's theory.
1. Maxwell's theory of the electromagnetic eld and the monistic linear theory of gravitation (L). Gauge invariance. Within the frame of special relativity and its metric ground form
ds2 = ikdxidxk = dx20 (dx21 + dx22 + dx23)
an electromagnetic eld is described by a skew tensor
fik = @[email protected] @[email protected]
1Received August 9, 1944. 29 2Proceedings of the National Academy of Sciences, vol. (1943), p.231. 30 3Proceedings of the National Academy of Sciences, vol. (1944), p.205.
derived from a vector potential i and satises Maxwell's equations
@[email protected] = si or Di = 2i @[email protected] = si; (3)
where si is the density- ow of electric charge and
0 = @[email protected]; 2 = pq(@[email protected]@xq):
The equations do not change if one substitutes
i = i @[email protected] for i;
being an arbitrary function of the coordinates (\gauge invariance"), and they imply the dierential conservation law of electric charge:
@[email protected] = 0:
As is easily veried, there are only two ways in which one may form a vector eld by linear combination of the second derivatives of a given vector eld i , namely,
2i and @[email protected] (0i = @[email protected]):
The only linear combination elds which satises the identity
D(@[email protected])(tDheise)
two =0
vector is the
one occurring in (3),
Di = 2i @[email protected]:
Herein lies as sort of mathematical justication for Maxwell's equations. Taking from Einstein's theory of gravitation the hint that gravitation is represented by a symmetric tensor po- tential hik , but trying to emulate the linear character of Maxwell's theory of the electromagnetic eld, one could ask oneself what symmetric tensors Dikh can be constructed by linear combination from the second derivatives of hik . The answer is that there are 5 such expressions, namely
2hik; @[email protected] + @[email protected]; h00ik;
@[email protected]@xk; 2h ik
where h = hpp; h0i = @hpi [email protected]; h00 = @[email protected]@xq: (10) With any linear combination Dikh of these 5 expressions one could set up the eld equations of gravitation
Dikh = Tik
the right member of which is the energy-momentum tensor Tik . In analogy to the situation encountered in Maxwell's theory one may ask further for which linear combinations D ik the identity
(@[email protected])(Dikh) = 0
will hold, and one nds that this is the case if, and only if, D ikh is of the form
f2hik (@[email protected] + @[email protected]) + h00ikg +
[email protected][email protected]@xk 2h ikg:
and being arbitrary constants. In this case the eld equations (11) entail the dierential conservation law of energy and momentum
@[email protected] = 0:
With two constants a, b, (a 6= 0, a 6= 4b) we can make the substitution
hik ! a hik b hik
and thereby reduce , to the values 1, 1, provided 6= 0, 6= 2 . Hence, disregarding these singular values, we may assume as our eld equations
Dikh f2hik (@[email protected] + @[email protected]) + h00ikg +
[email protected][email protected]@xk 2h ikg = Tik:
Dikh remains unchanged if hik is replaced by
hik = hik + (@[email protected] + @[email protected])
where i is an arbitrary vector eld. Hence we have the
same type of correlation between gauge invariance and con-
servation law for the gravitational eld as for the electro-
magnetic eld, and it is reasonable to consider as physically
equivalent any two tensor elds h, h which are related by
The linear theory of gravitation (L) in a at world at
which one thus arrives with a certain mathematical necessity
is nothing else but Einstein's theory for weak elds. Indeed,
on replacing Einstein's gik by ik + 2 hik and neglecting
higher powers of the gravitational constant , one obtains
(16), and the property of gauge invariance (17) re ects the
invariance of Einstein's equations with respect to arbitrary
coordinate transformations4.
By proper normalization of the one may impose the condition
arb0 it=rar0y
function in upon the i ,
thus giving Maxwell's equations a form often used by H. A.
2i = si; @[email protected] = 0:
In the same manner one can choose the i in (17) so
that ik = hik
1 2
satises the equations
@ [email protected] = 0 and
2 ik = Tik:
In one important respect gauge invariance works differently for electromagnetic and gravitational elds: If one splits the tensor of derivatives k;i = @[email protected] into a skew and a symmetric part,
1 2
i;k )
1 2
i;k );
4Cf. A. Einstein, Sitzungsber. Preuss. Ak. Wiss. (1916), p.688 (and 1918, p.154).
Angelo Loinger
the rst part is not aected by a gauge transformation whereas the second can locally be transformed into zero. In the gravitational case all derivatives @[email protected] can lo- cally be transformed into zero. Hence we may construct, according to Faraday and Maxwell, an energy-momentum tensor Lik of the electromagnetic eld,
Lki = fipfpk
1 2
(f f
1 2
depending quadratically on the gauge invariant eld components
fik = k;i i;k;
but no tensor Gik depending quadratically on the deriva-
tives than
@ hik [email protected] xp the trivial
exists, Gik
if gauge 0.
2. Particles as centers of force, and the charge vector and energy-momentum tensor of a continuous cloud of substance. Conceiving a resting particle as a center of force, let us determine the static centrally sym- metric solutions of our homogeneous eld equations (3) and (11) (si = 0, Tik = 0). One easily veries that in the sense of equivalence the most general such solution is given by the equations
0 = e=4r; i = 0 for i 6= 0;
00 = m=4r; ik = 0 for (i; k) 6= (0; 0);
r being the distance from the center. As was to be hoped, it involves but two constants, charge e and mass m. The center itself appears as a singularity in the eld. Indeed 0 and the factor in xa [ = 1; 2; 3] must be functions of r alone, and the relations
40 = 0; @[email protected] = 0
[ = 1; 2; 3] (26)
implied in (18) then yield
0 = a=r; = b=r3; a = (@[email protected])(b=r): (27)
Substitution of a @[email protected] for a with = b=r changes a into zero. In the same manner (25) is obtained
from the equations (19 & 20).
A continuous cloud of \charged dust" can be characteri- zed by its velocity eld ui (uiui = 1) and the rest densities , of mass and charge. It is well known that its equations
of motion and the dierential conservation laws of mass and
charge result if one sets si = ui in Maxwell's equations
and part
lets (22)
Faraday-Maxwell :
@(ui)[email protected] = 0; @(ui)[email protected] = 0; dui=ds = fipup:(28)
Since the motion of the individual dust particle is deter- mined by dxi=ds = ui we have written d=ds for [email protected][email protected] . In this manner Faraday explained by his electromagnetic tensions ( ow of momentum) the fact that the active charge which generates an electric eld is at the same time the passive charge on which a given eld acts. At its present
stage our theory (L) accounts for the force which an elec- tromagnetic eld exerts upon matter, but the gravitational eld remains a powerless shadow. From the standpoint of Einstein's theory this is at it should be, because the gravitational force arises only when one continues the approximation beyond the linear stage. We pointed out above that no remedy for this defect may be found in a gauge invariant gravitational energy-momentum tensor. However, the theory (L) explains why active gravity, represented by the scalar factor in the kinetic term uiuk as it appears in the right member Tik of the gravitational equations (11), is at the same time inertial mass: this is simply another expression of the fact that the mechanical equations (14) are a consequence of those eld equation. We have seen that even in empty space the eld part of energy and momentum must not be ignored, and thus a particle should be described by the static centrally symmetric solution of the equations
Di = 0; Dikh Lik = 0
(of which the second set is no longer strictly linear!). Again we nd, after proper gauge normalization,
0 = e=4r; 1 = 2 = 3 = 0;
and then 00 = m=4r 1=4(e=4r)2; 0a = 0; = (e=4r)2 (xx=4r2) [; = 1; 2; 3]:
As before, two characteristic constants e and m appear. At distance much larger than the \radius" e2=4m of the particle the gravitational in uence of charge becomes negligible compared with that of mass. [The remaining sections of the paper by Weyl are enti- tled: sect. 3. The singular case; sect. 4. Derivation of the mechanical laws without hypothesis about the inner structure of particles; sect. 5. Vague suggestions about a future unication of gravitation and electromagnetism; sect. 6. A free paraphrase of Birkho's recent linear laws of gravitation (B).]
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 57{60 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
Department of Physics, M.B. Govt. P.G. College, Haldwani, Nainital - 263141, India Received June 13, 2004
This paper present an analytical method for the heating of solar coronal loops by phase-mixing. We also discuss herewith the non-linear mode of phase mixing by Alfven waves. Under typical coronal heating conditions by ohmic dissipation due to phase-mixing can provide magnetic energy on a time scale comparable with the coronal radiative time. For large Lundquist number, it is possible that phase-mixing can attain a hot coronal loop. We introduce two model of loops; i.e., at symmetric loop model and cylindrical symmetric loop model. The magnetic eld assumed to be static and associated with only in inhomogeneities plasma density. The solution under initial boundary condition and the ohmic dissipation have been discussed.
Key words: MHD-Sun: corona, magnetic eld.
1. Introduction In a magnetized medium shear Alfven waves propagate independentally on each magnetic eld line when the dissipative agents such as resistivity and viscosity are absent (Browning 1991; Davila 1987, Nakariakov et al. 1997). When the medium possesses resistivity and viscgoestictyo,utphleedwwavitehs mpreodpiaugmatainggenotns.nIefigthhebroeuirsinAglfveelndglirnaedient (inhomogeneity in density etc.) the eld line come closer at points where the density is smaller and so the larger Alfven wave speed. Some structures may not be allow to propagate up to innity. Thus the wave propagating on neighbouring eld surfaces becomes more and more out of phase as they propagate onwards due to momentum exchange caused by viscosity and energy dissipation due to resistivity. This process is known albsusiteneuisymvncclitpgrttepthhhyoahraaifsossavsepsenitmun-adoamcggnehdavcidnxhteidsivuiatncniemhnsogglseisobsiiiippmtneney.ars)tsmeTidpcaogeahatrnenigceetvsenteiwtehetahntyeatniehrvcdataesunsnhirsetcobm1plerdu0rodtoe1slr.seq1tptnuTeccclirireomhkie1eoiesi0sdnlGys3hcetwietvhe.oilaennpevrtdAaemsiaislnsse(swmrdimapeaiesuaovrdi1tmeresi0ee---existing of phase-mixing and the number of wavelengths over which phase-mixing becomes eective depends upon the value of the dissipative coecients. However, some of the structure do not allow propagation to innity (or longer extent), such as coronal loops (or open magnetic eld lines) with more stratication so that re ection is produced in such cases phase-mixing occurs in time. This phenomena has been intensively stud- 1E-mail: [email protected] 2E-mail: [email protected]
ied by Tsiklauri et al. 2003, Botha et al. 2000, Ofman and Aschwanden (2002) analytically. The waves may suer multiple re ection in such a structure. The time of a phase-mixing state in which the rate of dissipation balances exactly the rate at which the waves are excited which depends upon the values of dissipative coecients (Hood, et al. 1997a, Heyvaerts and Priest 1983, Priest 1993). The concept of non-zero gyro-radius of the ions were introduced by Voitenko and Goosens (2000) with the creation of short transverse length scales in Alfven waves. The Alfven waves become essential in the sense that they have long wavelengths and low energetic along the magnetic eld however short-wavelengths across high energy. In this situation the ion polarization drift in the perpendicular direction creates a charge seperation across equilibrium mtenadgnteoticcanecledl thBi0s ,chwahrgilee sepeledraatiloignneadndeltehcutsrotnhe mowostions of the ions and electrons decouple from each other. A shear Alfven wave propagating in a laterally inhomogeneous structure develops strong velocity gradients due to phase-mixing. The strong gradients are subject to ohmic and viscous dissipation so that phase-mixing may greatly enhance the damping of Alfven waves and thus provide a viable mechanism for coronal heating (Narain and Ulmschneider 1990, Narain et al. 2001). 2. Basic MHD equations We are expressing the foot-point motion excite linear Alfven waves in the cavity of coronal loop and we assume to be inhomogeneous only in the x-direction. For the low value of (= Pthermal=Pmagnetic) linearized re-
N.K. Lohani and Lalan Prasad
sistive MHD equations are

@v @t
+(r B0) B1] + r2v; (1)
@B1 @t
B0) + r2B1;
@1 @t
mofatghHneeerdteeicnsietalyd,n,pdre1Bs,s0upr1ea,,rveAlatfhnvedeneBwq1uaivlaeirbevreitulhomeciptdyeerantnusdirtbycaotarirnoendsponding magnetic eld respectively. Here the equilibrium velocity is zero. By expressing the wave frequency space dependent in terms of Alfven velocity and wave number
!(x) = vA(x)k;
wpahteirvee kpl=asm2La,tahnedveLloicsittyhegrloaodpienletnbgtehco. mFoesr non dissi-
@v @x
The linear Alfven wave having its velocity
v = exp[i!(x)t ikz]:
The velocity gradient corresponding to x-direction
respect coronal
(i) Flat symmetric loop model.
t(h eat(Fd)ioie)rnCstihyteylin isdaotrincslyaylmlaymfsueytnmrcitmcioleontoroipcf mltohooedphemol,roiwzdeoenla.tsasludmisetathnacet
= (x)
aloncditythaenpdlamsmaganeotniclymeldovbeescionmtehse y-direction, the ve-
v = v(x; t) sin kze^y;
B1 = B(x; t) cos kze^y:
Flat symmetry loop model represent that the line todifreidtchadelliysctousryrombnaamnl celeotsroipcthsma(tHodvoaeolnd,iswehte aaatls.s,tuh1me99ep7htaoh)t.aotIsnpthhteehrepiclcayesnlmidnas-
idsirceycltiinodnriacnadllywesygmetmetric and it only moves in the
v = v(r; t) sin kze^;
B1 = B(r; t) cos kze^
by considering equilibrium state so that the equilibrium velocity is zero. We adopt the cylindrical coordinates rreq,aunadtaionBnd0czaisnainbndethowebetzaa-idsnsieruedmctferiootnmh.aeTtqhuuasat,inotdnhseB(p10h)adasenep-dmen(i2dx)ioninng cylindrically symmetric model.
@2B @t2
@B @t
Heqouwaetvioenr,cfaonr b eatwrsiytmtemn eatsric model the phase mixing
@2B @t2

@2 @x2
@B @t
fdaprbiloaomcevireneegnqetquxuagbateiyotoimonrnseot(rr(1i1ev22si)coceaar-nvn1der3bs()ea1.i3ss)tBueioxdttaiheicsdttlceyblreymtahraeontnyhsaaromitngeehthtboehyf attwrnhedoesmhiodirxeiiznoogfn.teaTqluhgaertaisoedncioe(n1n2td.)toerrm(1i3s)oafrleesrseismpopnosritbalnecfeofrorphlaarsgee-
3. The solution under the initial boundary conditions
Let us consider the equilibrium congurations in the form of a magnetic cylinder with coronal loop of length Lathn.edAhtZitghh=elyfLodo,etntpsheoeinemltesactogrfnicetathileclyloceoolpdnddleuintceetrimnagrienpeahdnocbthyoosrpZehde=riin0c pwTfulhhaniisclsmetlieoaiatn.dImostftoiomsveatashsgseniuntemwttieochetbooeabluzdenimdtahuretyhpaclloansdmdiriaeticaottniorfneosrtaatamtZpzli==tuLd0e,.
B(x; 0) = 1;
B(0; t) = 0 and B(1; t) = 1:
2 is the form of
vA2(x) = v02f(x);
wf(xh)eries av0diims eanstiyopnilceasls Afulnfvcetnionspienedtheintrtahnesvcoerrsoenadiraencdtion equation (16) can be expressed in terms of single parameter equation under the consideration of dimensionless variables (Hood et al. 1997a)
t = tt and x = xa;
Figure 1: The ohmic dissipation as a function of height
wAwahlfvevereentoasppeiresodp;tahgetat=teyp(aikclvoa0nl)gle1tnhgiesthtl-ohsoecpat.liemFfeoorfrorvtahtrheieastAaioklnfeveoonff convenience bars are dropped and we get,
@2B @t2

@2 @x2
@B @t

t d
L2 a2
is the time (
of viscosity for
vaerts and Priest (1983) and Ruderman (1999) included
a okwiniesminactoicmvpisrceosssiibtyleofforthtehefoArmlfvenwarve2s.vTshinecdeitshsie-
pation coecient changed from to + in equation
(12) by the eect of kinematic viscosity. We found that
there is no change in the solution of equation (13). Here
we also discussed, that the dominant viscosity coe-
cient is parallel to equilibrium magnetic eld. Howev-
er, for the incompressible Alfven waves with no velocity
component parallel to equilibrium magnetic eld does
not contribute for the heating of solar corona. There-
fore, the remaining terms are small and not taken into
the account. Also, viscosity can easily be included by
simply changing the dissipation coecient.
4. Ohmic Dissipation The presence of resistance in the medium by which the sedunisesreigpryadtoiisfostnihp.eatTwiohanveetahissrsotorucaginahstfteehdreecdrueisrnirstetonivth,ietayctuotrfhl trBhoeugm=heod4hciummiJc, where J is the current density. The re ection of wave propagating along eld lines also causes momentum exchange between electrons and ions. The time taken to
Figure 2: The variation of height with respect to for maximum dissipation
reach a phase-mixed stage, in which the rate of dissipation balances exactly the rate at which the waves are eouxhcsicimneitngiectdtsh.ddeisUesfpnioperdnamedtriusoliniunspimtboiean(clHotcmohooeneddvaiaetnltiuaoaelnyl.otxfi1ct9a=h9lle7y0bd,o)i.sbHstiap=ianteiZdv=eascsotebhfye-
mayBbyeuesisntigmaaptperdoxthimenatwioenhsav>e> 1 , the magnetic eld
For maximum ohmic dissipation
smax (2=)1=3

2 e
Above approximation is must valid Under usual condition g(1) represent
ftohreosh2mmaxicpation as a function of height for = 10 4 and as
unity. However Hood et al 1999(b) having similar result
ftohre wa=ve1a0m8p.litHuodweesvtielrl,ttohbereeinisclaulsdoedt.heTmheagmnaitxuimdeuomf
ohmic dissipation = =(a2!) as
Hs = 1=3!2=3a4=3;
length-scale of the that the amount
plasma. This equaof coronal heating
by phase-mixing are depends on the frequency, phase-
mixing length and resistivity. By integrating equation
N.K. Lohani and Lalan Prasad
(20), we get the total amount of ohmic heating under
considerable limits

Thus, under the approximation the total ohmic dis-
sipation is depends on frequency and independent of
resistivity. This technique physically represents that
the ohmic dissipation. Fig(2) shows that the height of
the maximum ohmic heating as a function of .
5. Discussion and conclusions
The Lundquist number S followed by Hood et al. (g1io9n97Ab). In terms of the size of the coronal loop re-
Numerically by taking the loop length L ranging
from 106 (Karpen
to 108 m, et al. 1994,
106 the
of maximum ohmic dissipation is obtained as
tmax s1=3 10 2
in seconds. For high Lundquist number S = 1012, wohemgiectd1is0s2iptaotio1n04(Wseocoon, d19s9o6f amndaxMimaulamrapehtaasel.-m20ix0i1n)g. Phase-mixing is the main mechanism which is responsible for keeping hot coronal loops, provided that the disturbances (pulses) are repeated severally. According to Narain et al. (2001) a shear Alfven wave propagating in a laterally inhomogeneous structure develops strong velocity gradients due to phase-mixing. From g(1) it is clear that the location of ohmic dissipation and their corresponding maximum value can be estimated. However g(2) represents that the hight of maximum dissipvedesnaaotltnausiesoeanboreydfiensaHpuceorb,neojadedscsetaeseont.dndaAttl!oh. he.oiighnvThamhtlluyheiceidasaopinsfpsdeirlpedvcaa.iitsnaicobdTonluhetshehweedsroiitgersrfhksooitnprhegdaateosigconrrbneaetadehssinoe-tohf aAtlfpvheanswe-amviexsinangdmtahyis gprreoavtildyeemnheachnacendismthfeordacomropninagl heating. It is concluded that the solar coronal heating by Phase-mixing is the dominant process.
References [1] Botha, G.J.J., Arber, T.D., Nakariakov, V.M. and Keenan, E.P. 2000, Astron. Astrophys., 363, 1186. [2] Browning, P.K. 1991, Plasma Physics, 33, 539. [3] Davila, J.M. 1987, ApJ., 317, 524. [4] Hood, A.W. Gongalez-Delgado and Ireland, J. 1997, Astron. Astrophys., 324, 11. [5] Hood, A.W., Ireland, J. and Priest, E.R. 1997b, As- tron. Astrophys., 318, 957. [6] Heyvaerts, J. and Priest, E.R. 1983, Astron. Astro- phys., 117, 220. [7] Karpen, J.T., Dahlburg, R.B., Danla, J.M. 1994, ApJ., 421, 372. [8] Malara, F., Primavera, L., and Veltri, P. 1996, ApJ., 459, 347. [9] Malara, F., Petkaki, P. and Veltri, P. 2001, Mem.S.A. It., 72, 574. [10] Nakariakov, V.M., Roberts, B. and Murawski, K. 1997, Sol. Phys., 175, 93. [11] Narain, U., Agrawal, P., Sharma, R., Prasad, L. and Dwivedi, B.N. 2001, Solar Phys., 199, 307. [12] Narain, U. and Ulmschneider,P. 1990, Space Science Rev., 54, 377. [13] Ofman, L. and Devila, J.M. 1995, J. Geophys. Res.,100 A12 23413. [14] Ofman, L. and Aschwanden, M.J. 2002, ApJ., 576, L153. [15] Priest, E.R. 1993, Physics of solar and stellar corona, Eds. J.F. Linsky, S. Serio, Kluwer, Dordrecht, p. 515. [16] Rudenko, G.V. 2001, Solar Phys., 198, 5. [17] Ruderman, M.S. 1999, ApJ. 521, 851. [18] Tsiklauri,D., Nakariakov, V.M. and Rowlands, G. 2003, Astron. Astrophys., 400, 1051. [19] Voitenko, y. and Goossens, M. 2000, Astron. Astro- phys., 357, 1073. [20] Woo, R. 1996, Nature 379, 321. [21] Yang, W.H., Sturrock, P.A. and Antiochos, S.K. 1986, ApJ., 309, 383.
Acknowledgements It is a pleasure to acknowledge the kind hospitality of PtTtehrhreoifsfc.oowrN-ooA.rpksKetrir.saotDsniuooapnmdphoyoifrctahMen,dd.(BDbA.yGirsIeotUcrvtoCtop.rAh)PyA.IsGniact.nseCrd(oIUwUllneeCigavAecekrAasnu)iot,tywhPolCeurdientgneye-.. Ts1u1hp7ap/n2ok0rft0u2tllhy(rMoauRcgkPhn/omNwRilneCdor)g.ereUseGarCch, NpreowjecDte2lh0i02foNr op.arFt6ia-l
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 61{64 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
Astronomical Institute of the Romanian Academy, Str. Cutitul de Argint 5, RO-040558 Bucharest, Romania Received February 25, 2004
The general results for the gravitational collapse of a polytrope are obtained for whatever polytropic conguration with index n 2 (0:5) : The time-dependence of the solution is analyzed and the collapsing time is determined. This is important for the determination of the time-scale for collapse of polytropes, which will be compared with the stellar free-fall time.
Key words: Astrophysics, stellar evolution, gravitational collapse
1. Introduction
The dierent aspects of this phenomenon encountered
in the early stellar evolution as well as nal stages was
analyzed in many papers. For examples, Goldreich and
Weber (1980) were analyzed the gravitational collapse
of a polytrope of index n = 3, the obtained solution
been useful for the study of the collapse of a white
dwarf that reaches the Chandrasekhar limit or for the
understanding of the collapse of a stellar core causing
a supernova outburst.
In the following I will nd the solution for the prob-
lem of the gravitational collapse of a polytropic con-
guration instant, to
for be
(which is supposed, for and the polytropic con-
cacoelnngtsartsaaln(ptt.hreeWsspuerresesu,sputprheoeswceeintllhtrabatel ttPheem=spteaPrrgaatcsuorn=esiasRntdoTftht)he.epToidlhyee--
dent while the polytropic constant is time dependent.
2. Basic equations of collapse
2. The continuity equation:
d dt
1 r2
@ @r
= 0:
3. The polytropic equation of state:
1 n
4. And Poisson's equation:
1 r2
@ @r
@ @r

where the notations are usual (Chandrasekhar, 1939; Cox and Giuli, 1968; Kippenhahn and Weigert, 1991). We dene the dimensionless scale z:
r = a (t) z;
vr = a:z;
wpveehlnoedrceeitnyzcepiosotfetnirmtieaislincodnebptyaeinndeedntinanad(tt)h.e Wwehoilnetrtoimduecedea-
@ @r
Then we can write:
Tthheefospllhoewriincagl-esqyumatmioentsr:ic collapse will be described by of E1u.leTrh):e equation of motion of an ideal uid (equation
@vr @t
@vr @r
1 @P @r
@ @r
1E-mail: [email protected]
= =
a 1 2
a: a
z a:
=a z2:
@ @r
@ @z
The time derivative of in the comoving frame is:
d dt
@ @t
@ @
@ @t
a: z
Dumitru Pricopi
We introduce the Emden's variable (with the nota-
tion of Kippenhahn and Weigert,1991) w (z) by =
There by:
1 a2
4G + 1)
:1 n
The continuity equation (5) may be written:
d dt
1 z2a2
@ @z
@ @z

or, using (7):
d dt
3 a
da dt
tainA: fter the integration with respect the time we ob-
= 0 aa303 ;
weqh.e(r1e2)0is=wr(itzi;n0g): and a0 = a (0).For the stellar center
c = c0 aa330 ;
where c0 = c (0). From (12) and (13) we obtain:
c c0
aa303 :
From the denition of w (z) we have at t moment:
wh=ichcwwe(zh)anv,ean(udsiantg t(1=4))0:tha0t Therefore, the polytropic index is
motion and the change is homologous. From (9) we
1 cn
4G + 1) K
and, using (13):
1 cn
4G + 1) K
a30 a
We dene:
Z h=

1 n
which may be written using (16):
4Gc0a30 a
We try a similar dependence of on t and write:
4Gc0 a
whiUchsidneg(n7e)satnhde d(1im7)eenqsi.o(n4l)esiss fwurnicttiniogn: g (z).
@2 @[email protected]
[email protected] 2 @r

@ @r
@ @r
@h @r
= 0;
which can be integrated with respect to r.If we set the
integration constant to using (8) we nd that:
@ @r
d dt
1 2
a: 2
and, using (7), we obtain:
1 2
If we replace (18), (19) in (22) we obtain:
1 2
4Gc0a30 a
1 8Gc0a30
+w z2
Since the left rbieghcto-nhsatnadnts:ide is
3 4Gc0a30
+w z2
where =constant. Eq. (25) can be integrated twice:
a(t) = a0 1
3 2
8 3
! Gc0t
2 3
polyTthroepsiocluintidoenx determine w(z):
dtehpeenfodlilnowg ionng
1 z2
@ @z
@ @z

we Ifnwd:e replace by (19), g(z) by (26) and by (12)
1 z2
d dz
dw dz

6=Fo0rthe=so0luthtiiosnisdtehveiactleasfsriocmal Ehymddroenstaeqtiucaetiqouni.libFroirum. Physically relevant solutions are obtained for 0 deviatimon, wfrhoemreequi=librimumco. rresponds to the strongest
Figure 1: (Case n=3) A plot of solution of eq. (29) with m=0.006545. In this case, zm=9.889 and w(zm)=1.6611 10 5
Figure 3: (Case n=3) The stellar radius variation when the relativistic eects are not used
Figure 2: (Case n=3) The variation in time of central den- Figure 4: (Case n=3) The eective temperature variation
sity when the relativistic eects are not used
when the relativistic eects are not used
3. Numerical results
Ffniacotor=crtonn32=m=ag0nu0w:dr5eaeq,thiuomaanmvls=ew=wti0thi:0ht0eh:01cf67eo25n8l.4l7t5or5wafolf1ionr0prg1rn7envs=das=ulyur1nee3, 107 K we obtain for the collapsing time:
tcoll = p6G1c0m
tti32nchoeatllinmf=odlel2tooc0wfo9licl:ne5=gn0t4vr1asa:e0lluc9de4feson:rsitn1tcy0o=,l3lrs1a=e;dcti1cuf3oosl9r,l :e=9n4e34=c05t73isv:e:9ecT8th0feoemsrevcpanerfroi=aarttiu0no:rn5=es,, polytropic constant and luminosity are plotted in Figs 2, 3, 4, 5 and 6.
Figure 5: (Case n=3) The variation of the polytropic con- stant K
64 Figure 6: (Case n=3) The luminosity variation
Dumitru Pricopi
Until this moment, we doesn't use the relativistic
eects in the case in critic value 9.74 105
wgh=cicmh3t.hFeodreenxsaitmypisleg, rfeoartner=th1a:n5
the electronic gas from the stellar center become rela-
tivistic after 304.836 sec from the beginning and after
307.977 sec the whole star become relativistic. In this
case,the star is a ic constant K =
trcaodlliu=s v3a1r9ia:1ti4o1nseacr.eTphleotcteendtrinalFdigenss7ityanadn8d. the stellar
References [1] S. Chandrasekhar, \An introduction to the Study of Stellar Structure," University of Chicago Press, Chicago, 1939. [2] J.P. Cox, Giuli, \Principles of Stellar Structure," Gordon and Breach, New York, 1968. [3] Goldreich and Weber, Astrophys. J., 238, 991, (1980). [4] R. Kippenhahn, A. Weigert, \Stellar Structure and Evolution," Springer-Verlag, Berlin, 1991. [5] Larson, Mon. Not. R. Astron. Soc., 145, 271, (1969). [6] V. Ureche, Rom. Astron. J. No. 2, 145, (1995). [7] V. Ureche, Astronomical and Astrophysical Transactions, Malaysia, (1999). [8] Yahil, Astrophys. J., 265, 1047, (1983).
Figure 7: (Case n=3) The central density variation when the relativistic eects are used
Figure 8: (Case n=3) The stellar radius variation when the relativistic eects are used
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 65{71 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
University N.M. San Marcos, Apartado 170090, Ocina 29, Lima 17, Peru Received May 7, 2004
In this paper the propositions developed in a previous paper [30] are complemented by the identication of some of the kinds of natural structures which develop from their dependence on NE-connection and from other inherent characteristics pertaining to them. Also it is stated that, although natural structure theory has some resemblance to other theoretical developments, it is clearly dierentiated from them. This is complemented by a demonstration of the possibilities for further research and applications that the theory oers, perhaps to improve all this a generalization of the denition of a NE is given and it is noted that NEs have no scale.
Introduction After the presentation of the general developments of ttbhoeeilnitsghtreteohcreoygknoinifzdeNsdE,osfthiNnerEeasfotprhreaetvthiaoistusipsrpieanspteenenrtdaietrdeishpenoresesc.iebslsearoyf porcoailnAteitsossnn,etoscoiefmscstliaahlarreyirfryuenlnaadantelidorspnteiemnbpnepibthnweagcessoeimznaeneNdsthEttehshmeea,rnreademmlsoaoatrrhktkehsore,focsmfloatomhrrieeepossibilities that the theory has are addressed. 1. Remarks and perspectives 1.1. Some general remarks Irbteeleiasntinodence,esnasneaddrywinteotedsrhaicatelliroecnno.tniacSteeinntbcreeattwteheeeonnrNtshtEe-hcoaotsnhnaeerlcrtetiawodnoy,. Adocaofnirudmerlecdaeltaintobtttineeiotrayn,pl,eoabnbsneseidtidrbwgilriyeeteescnoeftorlifort.snwoaaomIlnretooeetlrrhraaitmmnciotguonilorestenlhisdieepiirsnbettcteiohtttiiweoeesenxienaiinsl stuettbxehhnceeehtcmweau,.nenegiIinnetsemorumeltneitdfiotirireemsc.t,iooIfntaomln,eaoyor,rbimne outrhneeiedncirateistceiteiosofnoatnhl,eonbieind oirureecmntciooerneoaofltahonreroebenxreltiasmrittteyiloobarnoteeetnadwennieotdtesrinetNnlifeEto,sht-ae.ctumooWnt.obnhdeeAaicrtNltesiicooEst,n-ico.cNloneIEnaatrn-li.cesioscnIntntoenhtdteeacrntftaeoeaccrdnteiysaoesnnatritremieyltmaiefetobisaorrnmaNtcwEateooyscfoornmneecdt.ion arises between two or more entities, a NE is twoWdiitshtinrcetsipveectchtaorabcetienrgis,twichsiloef ibteminigghatreapcpoenasrcitohuast- 1E-mail: [email protected]
nntwieoehstsestbwhaehenriadcdhtthdhaeeeydrectaaoirnpedtahiccseoiptnyudstectaioobnulitytshioibannnekid,nbgeaacstbalbupeusretetostiethntehtirsientuhkanermoceerrectnnaaotnitin--; likeIat ablascotecroiuulmd bfoerwinosrttahntcoe.comment that although it cwsisooomuruelledldapteblixaveiceseot,pnatolbhyssietooiolnounentl,eyenbppteooictssayiittuiitsoohennis,tpoibnoysdtsonhibeetlcheesaestsntoistibeytetiwhsdoaenutteelicdrfmetsbhsienaeerriynde tthoeeaexchistoetnhceer.of more than one entity to make reference nseeqcueTsewsnacoreirleyomfhaoarnvkelsytaotbwobouetsctpoernpotscineisusso.aulFsl;irtashntaldyt stiehscaontneicdteldsysoaterhsyantotoat makAesahparsocbeesesn. stated above, in a general sense natafcuuiranerledkaieimsnlddecsnoomtafalplsNootEhsNe?idrEdWsetnoohturiilnrdeagltyshepxioseifscbtina,ealwrtkeuhilrinacatdhledsoitsftrouNacEttNhu?EereCvsoa.orcuulsBdupumeataNnEds/?or to Einsteinian space-time, and are these also mmaigcAhrotnooNtnhEleysr, bpienosatshibseuilbiste-yunnsleievfetthrsaoetp, etnphaeristunothifveearesgxerieswtaeetnerckenNoowEf (Nh(qtauoEhnlaeesdssa(;uprsnsutehibraveh-neuardfnpsoeisrov)mt,emhreaesarerntswdtc)eoorbNsu)ymlEdamo-nclbeodoaegnnisnctosehaucolertfoceewbednjhteowricftytiesttg,hhhaeoatolneetedshxfeiaotsrhnrteedseninlmbcaeeltaritlgcaeoykrrf wFtohnooerutclehdexenaibtrmerewpthaoleyef iseotpxuiiirsttapgolrafgotaobeluaafrobxrlsieeuesbnt,h-eauarngntdyitvht(ehaerrasneetd.atphrIeetersbmhelaaigpgcashkltamhxaoailelstesotsearbar)eet. pfguaontsecssitb.ioleInt,thiis.aeta.,lasaotctlpeinaogsstsiabslotlemertnehaoatftetltyhheaessseebhaoortlehesceohnmatvrbyeinaaendddowuebixtlihet
Walter Cabrera-Febola
wtwoeremnhtohleems w. hich make eective the NE-connection beeisrthyIietorfiasrNcnhEeycs.,esHwsaohrwiycehvtoemrrisegifhnetrceatpothpoeenamer eotaotnhbienergpoobrfovbtiohauibssl,etewprmhroicpihsscolamrWiefwyiththhaatrtebslNpuEercrsetdwtoiotuwldnilibltbeeneeansnsit,aeliytbzeaecpdapuinesaear,ssspinneeccceiestcshasertyyudetxyo-. intwswothte,iectmnhheetcyrhogeauemrldde.idbnOiettoeihnroeenrnnwetiiitaaseetn.eotdIththferiersorem)a,wlsceoorauecplahdotiosbnsteighbeolbreno(ltuyih.neao.dtn,atetrhhieeeenystfbiaatrceyet-, tiugthinnnawiintvtieielan.lrlsgmlTebtheoheaereinrnseegutlahebvrmaueetnresyainovltmtlesirNnesoyeEpf arisasonhNpidnaoEvtsheinmteiaintouebnsi,totsbuiwbusnethedxisNaciphnrEayc-snectadoainitntndenhgtaeahicrdtteaemattdhobuuutesosrtbmTaceuocredopenktli,atoen2f0ctae0ht1iet;audnSneytiseveitnerivrmhseaeesr.d(bKteSihainnongcudecroyTtn,husOeridovnekrrue,ewt2d,0Ste0hkt2eep;iyn)rnhoiiasttriecgdn-atce,iysnascinlnoidgcr nfpeisodorloctlobopownyofsssititdtwhHieoeoornerubsdanrviiatnavhnewaaerstnsh,editchiuhfWinsittdihtteweitrseounitntbhsi(rev1ape9ncrr9eaoss6espeaoai,sspiit1cpt9oirio9nson6assibcd.nh)eiTtraaeehnn.diddsbAcomooltuslhoolnideddreiest-l ttcohauessseeeppaitrrsoactseeespsaagrtaahiteniobnwrahhniacehss tcmoanacknoeomsteistetpoanariathete.alitBnieninniogtredlcyeyrcblteiocatifisnaopcpaitnrnto ihtannaeciithttsyeieatpdsgbataoaerieatgnseti.n.innIsongIttnaoomdtrehdexeeiaptxniampontanodhn,dadtmenoilnessiagetonpmtisasoertatshihutnaeiptnpangiotnitsidiyses/.dibonrAetghelnixsaniopttneatti,nnhhidgeet mtwoinoiellnmlynoboofrnttaehbneeeesnmmtaioretevyme.imnbrSeanenncitteoeasn,rtdbehunettyhoetwrifinsaltlctnbthietetehtb,oarbttaaenloclenaysuemisnoeirxtihfemdesoodbrtieerhieneocyg-f thtbishharueaavtnnecenotasehmcaeceprosweousnaihpnreoleynl,entoseieftqnoeiufttiaissatlyalndyni,iemsiinnteitinmnittsiyiaingol(ihnstttuesh.bpeinepBuosununstiepivdtpteehrcosdeoseneofdedianscitttontiohtobnhitesawmcthanetisiahctehnee),egryttohhbaerarteebhloiiyssf wibamtloomusruesdolteedsmrhtsmasevbmtaeehdipabenttogytra,hdeacnemhsri.taiervsAaeiscnrlultyetptrhdhpiisieostsiaweccbduaoo,ylfvt.teaotAodmblosmeeoemsomivfbneerto.mahtneIbeenxrbiacrasnladutendodseiesthtihataohevrnyeee, pseonssseib)iwlitoyulodf eamnbirnacneitaellNotEh, some way (i.e., tahreatOcenonemtiptinoeasseldcpaonoifnbtesuwpboe-nretnehttritatioteesdbe(bi.mye.eo,nthttiheorensyebdpecoisassuteshsees tfhealeceyt-
mmcouennsnttesc)bt.eedTboernoptkeientnieetsrdacotawennabnienepnsutuittcyhawtahaeyw.NaTEyh- ticshoamntneetachntesiotNnh(Eas)tipfafaroceastsncitbohemlanettptietooynsbteiidestipeocseofnmcNeaptEnro-abscteoeedndfnoobelfdycteoaedndnloyyrsuoobbtneh-eneetnretlieeisntmioteiwestn,yint.bgAietitlnosigsothntthheoyeet fwmitohleidesairnnnesgottthohepraoNtbsEseifin-bcdaloeninntgneonepctbitoetiysofsnoiibslsdlaeferodetr.omoTrebdhbeeeornmeftfa.oodnreel,yitnohnitsehceealsepemlaaeclnseost 1.2. Some similarities and dierences with respect to structuralism, system theory and complexity Siiswsstomirtmnuhocaetttnuhmdtreha/aesloyiarscmcmasoyesn,essu.ttineodmdIettrehrttmlehhyeaaienoytxrgtyNheeanEnavttnseidttiysh/ceoaawrrtthbacbiriocanomhnthsccpihomlaeuoxrillefdiatsyrbcti,oretbuinetuccsetetrurwmtnrhiaeetilddhssa(atCnsrdayuwscWttseu,mer1be9;os8tfbe8tur;rtaP1ns9itsa8rfguo9ecr)tm,tu1dar9eat6vilo8iisan;mtsRe,osircwkfarhaoisrcmetht1odt9hfe9ii5snn;teeWensrtnesitabtrylsutrcewetrlhua1ter9ieno8na2isst; tf(awoapirskatmtehrrstuaswct,aithsoueanlrfetesum,,nceoetdthnuacetl)mdsr,ewebbnchyetoiacncshlsoottnmmihtfoueeaueyo\nnofatdsccii,cttnuisgoerntrtceash.s"m)eulo(ttrhnwaeignlhnatitgtchicho(ehsnatmmsrr,uaaeccmtkttreeuabrnreuiesrsp)-stietnihmcdesai.cttahiActraneelseo,,tlbhnoaeagrstiiuccdarialplrea,ornwepdnhecrilletienieigsssturtaiuhsttcatitrtcuibNrsuatErltiuessdcmatrubeery,mesasb.strrtauFhccieetnisurarmlanlylaai,mstmhoe-f twataoirohpensialtperrtrtuhtoihcaepteyleuorormtrteihseal,esiymroowtninwtelleyloydl,wbotehfrexaotspneloernsmnoftope.ersemssMrptasioeeetcresiieomooncvsfaetNtnrho,dEewbssse,eeitllafNoh-nnrEdregesgsitupntoloeaacNtodtiEnodtnlsiyo-,, ttRrhiaecnkdsafirotremr(e1an9tt9i5op)nr.os,pothsietrieoniss onfostcrluecatruraaglrisemem, eanstshboewtwnebeny trhesaptNecEittsss hcweainstthcraethrlteoadbinejescnitmit|iiolanraiotfiNeasEswy|isttheimssysssietmleemicltaetrdhienboyrsyoK,mliiner (oitws1hnh9eeaa9pt3otr)efao;rspmsheyovosntewtehreenaamvtltespriisoso,afsvsissniiyrbKtsclutleoieanrmdltlareyaltsshnnoteietomtvioroeyarna.kseeNTxsopEfhcluliaewcsaihstriylt,iycshtitshdemiiensso,dnitsewecdohlnneibecaldhyyr ifsaneerlreedacnettctheaeedsirl.bbdyMeitKwoulresieeero,nvwweaNirtyEhthasrseearstenphdeaecrtteshptseoemcdwiaehlclaanbttiuitaoitrnoesnsirgoeonfffeiararcesasdynyststttoedemimifn-. Twerhitaihspiptteesramirnttreoerfnbearesltrtweoloatthdieionseesrteonortrcotahnrirnnaegncsgt,ieoamnnsed,ntwitohifiscahnsohytoscwtleeemavr-,
wtaehwrmahtooalerll.gatBhnyeicscewotnhhtorinlaegs,ts,amnindeatwhneh, enctaohsreerwothfhaNitsEiisss,mdevieseatrniynttchbtiynfrgtohmies caaislsesdaayirslttyeeerrmdmene,twtnhfheriedocrhm.ebMmythaocekroeenuosfsveeiertrrsoinfsmygtsehataeenmdwiengogtrrhedmeeo\oortryfhegiundesgnie"esurai\snleti;htNyitnEhogsin"s, wbgprurheoteaxrntieemosittatatdiessisaunesraceeetdnnuctrjereua,silstbttewehcrhaamuetnsaaessNNoiEmnE,essayegssxetdineseemtsrcairntlihibtteyehoderisyar.ebraeoBqlvuuweti,oraterhpdlde-, (Knwolinhr-ar(te1ea9vl9e)3r. )itdoisn),otwehxiliestsiynsttehme sr,eaalswcoorrlrdec(,ntohteeydabrye tdheeIntneitriamodnd\oictfoioamnsm,yisottneimssewnwsoher"itchhbychoeKmsliemrlewecntittsih.nIgrtefoseenreemtnhcseethutoasetthtooef aifnacmmt ataththheerememaaatrtieciciaaanl ,ltoeatrmdoefsdinseitsiinomnitpiwolynhsi\ccheostmias bmnloiostnheessdetnaisbnel"ios.hrdeIidnnmeTnsaohturtaesybyptlrlbitaoseevnhlligeeddusyetaoaiagunbedlmh,iesobahwetnehcditate;oiumowscnaeha;tliittclcehhuaielalsayttleiedosrtomstoohnsmfeoasterwotet-haecsiylanilmlgyilne,opdublwyudwhtfeohitcranhhmtietuyttihholadenasyots. sKvvoailemgiwrueeatdnhpoeipnseesgsawrinssho.iitncThianhivesdaaiflcaildtscioatotnateahcriaotytsmatsmhncedioendnntefoietanctiinutniroaeantosucsfrieeeml,neactntineoydcrsrcbietiys-eunsetidcindtehenidteionnsiti(,. the failure to dene key terms citoymNaplEsleosxitmteyni,gdihsntttohhwaavtaeridtcsesreateasuinnniaftecuaartteuioranessooifnnenacaotnumdrmecooinmn spwolemitxhermfeersiexpnteutcrtvesi.soiHfonodwitheevareternt,trtahsncesice enancvdeossr, aowlflhcsioclemieNnpclEeesxs.iitsyaisttrhualyt odfifaplexMitoyreiso.veAr,sitHsoeregmans t(h1a9t95n)obshoodwys,knsoevwesrawlhdaitecroemntdtieanhxnegaa,otcnrtwiadltyhieroriednleseedseaiopnnrfcaechtdtohhemera. npwcdaliessxfheriotmoymfaeNxytihEbsetser,,eiawnnechdvlaueprtdryeaatdchNtiuincEngadlieelsylrshaeitnasfsyohtlbhleoeaiwnedngs- 1.3. Possibilities and perspectives Udedinvtienirltsone odwielsdecrsie,enndtceecaolhimnagps abwretiemtnhednntiavst.iudAreedltahasonudifghsietpthwairesartpeerddaciivtniitcdoehslwopahsestocsi(howamcevepesreaboedebvctlhoaemenmttesar,gaeaeewsssa,warnehrooeetnfstuthihltteicstfo homraeewesvstih)st.aioovStnehotomerfiseettdhureedtsoyewacohrofcorvhlreeeercriysts ihotnabvenyeeensnsohtoafannlcwaitnauygrsem,buaenletndidtaihsdceeipvqliuisnaiotaenr.yofwTiothreaks,raebsuuttantitithnye,ghroaefssutblhtees-
cteaonsmtksecbioyefnstptiuadrcaydminisogcuinpnatltinuimersep,aobsrutotannbecy,end. oeNtveEblysopcisionmtgabakiinnniegnwgudvpiistiheorins-
carmysWstearhlisiocuihnslimys otaellemscouprlteeesmd, atborrkatairnbysl.e"ainsdthhautmNanEsgrmouapys,habvuet
I a
199N4,E1s99b6ri) new ideas and the possibility of the ap-
Walter Cabrera-Febola
paunrpodathicmheepspr,oocsvaseinboiaulinrtdyknwoofiwllnlepewdrogdmeuoacftehnneametwuartiein.csaiNlgEhdtessvaetllosoopdmeoepepenentnss tpttohieoeandorserssyactnhrwidabitlepltedtorhophiosatlhponesgeywgj,oebcpna,uotibiennugteotloyrtyfhnveteihyweewmod.rayeAyvaetrnleodqprusmmtireaesnyigtmbsheotwldaiitiltltacibpcaee-ntn(heeesecwpefesoacsraniamralyllu.yylsaitWtshioeointfohooninfledsnpeophwnrieeloass.sexonipoTtemhhdyes,,hstaetonruoedd,)yptwheoierflhrlesabopeimss deaseclovsofoeplteofhoperfeosdaer in forthcoming papers. penreatldcOp.tunicraAtehl aeacnpabdpsaelsiaicspianpotilfpoietnodhienissstcecimelneneaicwgrelhsyitnaobsnpiegdehntit,hnsbe,tothGhtehe.tpidenoceshtshnMibeoiilsdloitigtryiaceloar's-fl dKleealsirbingannmeoduvc'Vshe(ml1c9roo9r'5es)ahcboloaouikmtsstahwneidtshtlroeronepsgpsthe(cJtaanctdoobstsch,oep1en9e9oe6fd)entoorzltasyhtylrimconmongemogmsdleyiemealm-abiblooaueruricyltdtiassainnsehgdxaopowbrtreiheossaelusorlegtcdrieeoslltlfbasytsbetserdTuhusriacpistvmseueucmrsetaseli,tnrrhwe(arsh2teei0sac0phwr1cohch)noa.s\uteSSldmeotvmoooenrsea-t-dtidsuryurbnnglaoemdcokriucepdadl,ilosyber.audLsteoihkwieosnwa,nacaoonltlndwntnhehoecetttg-hwtehenhreee-stdahnoaeytnrsdpa panipryrtobistcieounionlgaklsre, itpnghrteeoenrtseaeticointsrhidasyneotlephtimnheitenefeiarrrgpecsewtrtsootitnhfrerkgaootmmg(pEriroctzowshzteeiewlnillnhg,inse2rka0eesr0l.edo2..n),"a.esnsAeOoetmlfwnsotbohtlriheetkdisictmiohnruepetlsooodprrnyetbc,eaettnswetowoefpmhrskoaossitnmtttiooess bntohfoeedrceeNolsamEtbip-eoClinensms.gIinentnhtrgeaeearenyllieetrtmyao,leNnnwetEhstswi,coohfwrkNiwtsEhoaustrlhdeaenmtdapekotaishnnsegibtlhitilnhaitkteysnaobosfptetienahclgetl opcthafesertethdsaeiimnthieneragernnetteotNewxaEoasrpm,krspobplumeetsratatyyhllabooteffcNGathnENesmbE: esfspo(esriecemmkee. dbmAeuolloprsweoi)tsi.tncraoFsnnorogmbmlyee claauhnlslodaosreNicnnoEtmo-hCtephsoeornonsweenbiotnysfgtiNnthoEesot-cChmelesle.bicniPaowsceehrhsheicamahpriescw,areelalhrtaeatalevecdeatsitbothynassrot.emtaThceeht,iecoarenreles-ftpoaoiroereeisenra,atcnNscoeoEfnwmevttpiiwhnelwiesosiorh,grkheyindttshobteahyoneinrsrdysewtsabwoanulyoutrtabkifpoortpotnhhmrseootwaroacyoh.raskolTtlimonhtgheettsehhteeoeipngnsogetatismthdsiieiebersielemtirntheitanaeiyttsc(At2hal0nas0otb3aie)tr,seWiesennawottoitnsrstcBahanaldoera-fSfbrnteaooestgiiannatengztdw(t1hBo9arok9tn8sta)hlb,iekearaeneudcar(Sry2ets0rt0soao3glm)al,taeBzttea(in2rcat0eibs0ta1ioes)sri. w(tBhheaorpsaeobsdasaisbit,ial2iat0yr0eo3if)n,icmwopnhrciloleuvsianivlgleotlhfiketeihrfekomnoodawrwleeedbNgsEeosbr,ytthhNeeErbertfoahriene-
ocinarsyttiaoisnncscelientaersnloysceiogaprl,ietenyc.odnIenovmealiodcpdaeitdniodbnoy,tthKhe.errSenecelodlsuso,lndsu(bcSehnaealpsspoflonir-, 2aaa0nnn0dde1nDg)tr.iaornIewndstgthbbreeucircno,tngu2t0rare0op0lpd)li(isiDetndr.iwbtIonhugitscebthsuergad,anieid1sn9bo9imaf8lc,apen2ollc0rute0las0an;mrclSeei.fctehhHaoeunrwiaigcnaianygl sih(stGarvweNesoEsrew)tshh.wathPtoiecmrghheaainyspeasrbantelyoizceeianmlttlpiehtdreyovdadeeegaennlnlietedtirhoaenelxseaoncfadttaleuyvrNeaalEsol p,asmttNrhueuEncsttbsuwurieett rwmceoalenaynsxstt;isint,ugirntssetodt,mheibeslyerwmeaaqenyunyittraheernmeytbeitpnayatssret,thietcalhleteimsswemainlratlesybnobeofettamhtGehaedNbeaEbsianicscae,tnhperlbreeiee-mbrmeeleeqaeimnnurytgiernieutnthnseetelioetrysmtatinhmetgoneetci,atnohrasryeltrleepeatsnahpdrteotiwnticychdolaieminstngpwwapciinaollllisioneabn.tbe.aSitdnehTedceaohosrninsedost,fmpheeNaelcteaEtmnirsvesee,qwnubtthihaaircrasehyetpbansyaoprtateieccbltleseemispneeagnrrtteianaitrsnhyidienepgbaoartrtosieocNuleetElssesimd.aneeTndihttsi,trhrdbee,umitetanstithnbiteiaynsegenisaetillmtelymtahidesenetmosbtayhadreaeer baIc(tAobemiosnneudpgetemliirtnssshhoseientddh,ea2brtos0ytr0nTo1aicu)nue.tdrsneisexderaec'msoitnip,ddlieenascatoohsffeissGthcwNaeisEleelxsbwtaeehrnaeadtcetcihdsoemionorpdngliaeicssnahitaesemdcd-. nanoysOsccanaleele,,nia.aelt.l,hpoaoulilgnththwoenoaerstpphoesctsotisbbloeef onibtotjaeercdetiioasnctchmoamitgphNltiEsbhseehtdhavaaett ictafhoreiuesll,nedmaobgteeantihtanae,rloywbwaepseeharraestvclieecamlleGeseNwnatEhrseesorewtphehNeneEirbnesagsedelioenmentleeohmntistewawnrotyarsykp,iattbhrttuehitcealtrecoescomplishment of all the aspects of NEs to any scale. 2. Appendix Here some kinds of NEs will be listed; however this list not necessarily is exhaustive. eenactih2t.i1eostRhceiagrni.dnlToythNecEhd-aecngogrneeneetcohtfeeidrrigmpidoeiastinytsiowtnhilalwtdiNtehpEe-rnceodsnponenecctttehtdoe qeTancuhttaiiisnotitnmeistoaycfyhoaoafnncyecgueorottrhhatseerirareeqprneuotsisiurtietyltdi.oontfowthmitehiarkroeewsptnheecatcNttioEoen-caoocnrhnboeytchtteehrde. eonntohttieUttrihnewseriyigctaihadnorleyucthaNabbEnleeg-cceotomotnhnirneeeigctrutNeprdnoEs-mitdtoiieosatcnnhosewnintrithehocarttriegedNsi,npEaew-lcchtopentotnohsieetecriatoecondhr. Ttthitheyi.senTchthiateinedgseetghirneemepoosfesilutvnieorsnigocirdabintyybtwehieilnladbcuetciioendnveobrfysaetnlhyyeroeatlcahtteieordnentoo-f
tcphoonesindteieocgtnre.edeTowhfhereingchidlaeintsysg,eeeninotirtptieoisssibtrieeoiqnnugicrmaendoratelosuocnhrbaiegnigdinelydtuNhceEeidr- moneenTtoootthfaeallrnyeedlniertmeitceytnlyits.NdiETre-hcceotrlneynNceocEtue-ldcdomnbneeeacentnsetdtithiwaetsitehivnaertwylheeailcseht-
btchoymistbheienntaeittniytointbyeoifmntgahdedeeenuntpietdibeysasuthntedheeNr Epcoo-csnossenisdnseeorcrat;teidoorne.bnytitaiensy, lwaayrrheeiNTctrhEohitg-eaacirdrloelelnyyanarreliNesgcotEiNde-pdElcya,osrnNtawninEahedl-cilccytohpenduaan,nrrtereiciaagtntleioldddytlaywprlilaNhgyrieEtdrnii-lagycalioldlynNllnytErheio-cegcrtioeedunldlenny.mreicNNegtniEeEdtdss-ccisoonnannceeoccmtteepddlebwteehinecngontathtinelueiunamsvterbosneetewweeitleehnmtrehingetiduilnsyruiagnnirddiigtuiydn.lryTighNideErlye-
adeallnielromettchhetenleyrtesoNloenEmfe-a.ecnnotnesnntaeicrtetyeddisirnmeocettaldynisrNetcEhta-lyctoNantnEel-cectaoesndtn.eocnPteeadrotfwiatilhtlhye motehne2tr.s,4tohTfiosatnmaleelynatniNstyEth-acaroteneNnveeEcr-tyceodenlenmmeceetanentdsofwthaitnahteanattliltleytahisestNeolEnee-cetwhonienttirhnteyeacitnstoeyadbtoettloehaaetsNrhtEeeol)new.mePheeoanllreettmia(oetlfnhlyttihsNtehmEaeu-tncstoitisntbynneeo(ctitt.heeNd.e,Ecmt-ahcesoaeantnnfisoesrctnhtaeoadntt
NtazoeErNao-TEcmuohnnewirnnhpiiegmioccistdhuselemdyiss,sNoow1rEr0itz-0cchea%ornonanrcomihegfcaiattdnxehlgdiyemeoaNuittnmEhsde-dcroveofig(nciore.neeneev.e,ceotwrcefsodearr)ircg.weaishndpeiottnynaldiaktisnoigasf NdstcihoidEenee-nrlcraeeoevctnntietonelndeloce.fatveAteidtlntsshwoeeelfnietltmethihvteyeeanltemtoanlfaertysaiytosypmtbaesoerhnttoooiefcutllaioedtlstsl,hybpebeaNrurtEtetasl-pkeccmeaoonrnemtnniianpetl)ctol.otyseedcNTdoEhnaoet--f
ctthoonattsheteqhureeensNpcEeo-nocsfoenintntoeecrttnhiaoelnaaiccsttiirooinngisdo, fbouartnnytohtei.sntdRitoiygesiodnritoyetnrmteifteeiaernss mltyhoipsleawcruatilyaeslal.ytAaNnllEel-encvtoeintlsyne(icis.tece.od,mfrwophmleetnietlsiytetilosetmaNleElny-tcoaorrnycnopemactrpetlidectleiens-
lpcironiaogcnsitasdhatelielsystdseoNwrroEat.uhy-tTcesaohiNdcneteEniNne-occEgfot-enactdshnoneeeecnnxtNettiiceoEttrny-encdbaiosylneanetnhntebitectoitituneeisedsee,sa.ooenfnfAdetunixtnthtireeeeixrsgpnaiadoamnsllyspdteolNseotshElooser-f, ceonntin2t.ie2ecstSetcdraonennngtoliyttyNbaEen-csaoerpnmanr.eactteedd meaesainlys tbhyataNnEot-hcoenrneencttie-d ttceyhonnetoinWtrqieeecuesatnaekntcdliatytinieteNnysbtE.ieot-ifcTesosheen.penaoedrrcaettgteerrddeeeqmueoeaifarsenisldstyrtethbnoaygttsathehnpeowatNrihallEetred-ceeotpnhnetennitedycNtoEeondretchnonetitteiineous,rutbmreeibnqegutiwmreedoern.eAswtsreowankigtlhylyrNaigEnidd-ciwotynenathekcelytreeNdisEtha-cecoonlemnsespeclrteetides
tcaoonndt2nh.eie5tcstleiIoevtlneeslmewoeefhmniitctsshs,tlihaistargttihessetththoeenerleeemfatisehcntaatttsh)es.axptiescttishaelbekNtiwnEdeeinsoftaiNgNhEtE-lipytossjeiotlieinomendenNttoEs,-ictthosnisenlkeeicmntideonnot.fs.epSSiipinnlcoceekeaamNNaEEy biisse ccteoormmmppeoodsseecddomoo-ff NectlohloeEwrnmosen,ureegenceahttlicseohdmnoisf,eunebwbrtoeh-stNnihc(tEhet.lgoawity.,iielmilrtssbhmceetoeoNmdcaoiEapnn-toyncesoeleyocndttnihinobeefcnyretreotwidohfhritwsihecikhletehimnientdxefhienesorttfisosoNtrahbnEoeedrr-tciotwatshseeeeesrnletwmahineelrlneottrosig,soa.iannmatnhudetuiasteslndasetepomethnsad)te. nIicfteosbeneeemtwdseisetahnpaapt eNianrEssoatmnhdee
eapInnnotsoiasAtreridlmsesessoor.. ritF,noomrttheaisniyststttcarhaynesecst,etotrithebneirsgeNtaehakEs-oidcefoortwnhtnoneescNtethpEeedacrNaoenEtnetn-iceatoicenhtsina,oienroc,rttihttohahnines. mTdehugesrtepeboeossfdeossstnoreernumgstiahny,g baexlusttoertanhcaitsl tidnootoeelsrsnanasolltyinmdtoiecaacntheadtnhgaaebtottvhheee. NaraicngEcyio-dArolcndytoy,ihnnsenNgtrerEcotetonnimgtotilnathyyyei,sabnifafeodutsNrhtwrEeoewr-anecakgoyalnsyorn)enl.eiecsettTnoeetrhdditinsiiaoenbswt.oaiovlnlteyhae(clrsrooimgthiabdapilnnpy,alyNtuiEotnonstohthate2r.a3reelDeNmirEeecn-tctloybnenNtewEcte-ecedonnanttheecleteatwdstompoaerratnmiasolltryhe.atthathtearereisNnEo-
dareep2ecn.o6dmTophnaecrttehaeanrddeistitnwaconocmsepspeacbiceattl.wcCeaeosnemstpohafeciktriniesdlewsmhoefennNtstE:hsethrteheasiets nilinanottateferrrbieooeirsdsoypwfaohacfenenweianntthtetierthryeel,ikifineostrtaehirtneiosloertaanonseftcpeaoonnaseietbnefidrrtediteiynw,chaafoivcgrihltayinshssia.ntsaTntthhhceeee iigacntorntemsdeeer.peigmooTernnsheeoetnrfhatciaslot,tsmotfabhpltoemahnceofetossnNrtemjEsuasensartsynhwrdoNeiufEttelhhdrerisfibnrleaeignetccttoceooanrmvstsipioodtamieaecrslteel.dtodoIfaentstseohgsrmeepmmneeeic.nrdiaeIeldnc-, tctchhooiemmsdppsieaasncctsttaenneencasetlsmitbiyonetscwwtrieaelalensnbyineiNgtmsEaoesrnwettiihlctloeibemdsepiisgsateaclnetnestcsroeearltb-,hientethcweeoxemdetenepngatirctetsteh.eaoAlt-f
caaorreennoNenEcet-eocdor.nmnIoencrdteieredel.ecmtlyenNtsEb-ceotwnneeenctethdemtweaonosrtmhaotreththearet etNhmEeenrdetilssattiasendrceetdoubaceetcwdo,emebnpeactochtmeNienElgemwexoetnurtledsmbieselyzaecrdooem.nspAeacNktiEnw,dhdeoen-f
Walter Cabrera-Febola
ulynneimtdeabaryneatthooerbnveoumlmuombreeer.cooTfmoeplbeamectde,neatnslstephroerduoguhensiatnf,,aIins.neeo.ts,inoabmfdeteeenarecsnacittoyicmteiwreptsiaallnitnhiaeildpssoorbiebnylteaataainnonniiisnnnhcccirrrpeeeaaacsssoeeeuiliindnn cthome2tp.w7aoctTpnwreosops,eorurtnietmsiloinarecnroeetanhsteeirtiteposgoeimnthtaeyirs, braeenadcNhsEeod-oconant. nwechtiecdh bdhNyiaEp-emsdreiotsnrhcteoenrtteynhpeaccenotsiunologdnrewbaNnietyEhs-occomoonmneenboeNicrnEtaimsotinoot,rnheoaooftfftaththrheeeeiscrtaawmepolaee.bmtlPyeenpeotres-f, asetohlnemedmmete.hnoetfnothNreEeml-ec;moonernnttehsc,etyionrgcocaougnldatiinnbueteoatbiotleoexrtoitshtreewmgietnoheroruatotteiottnholyer iainnnttdee2rrd.mv8aisiNltastpEeopn-rcetoaa. nrTcnaohetmcetyibinoitannerasretvmiaionlanstyeo-rafmelsititohthtebeeerntwtirnoewtg.ehurTemlanhriettrtoheerefnoyitrroreaerpgtnphuoeelanarerrwpolareirlallayraa ilnstooticenekrxtmeiosriftvttaibenlisntr.etdr,Asmi.rnriteTetgxehuanelmtsaeNrplylNEesEimnwstiehgmrihmcathyibtatebpeaepntestahoerorrmaarlneeogddfudlriaessrhgalupeys--iaibrnnerdicenueggcuaelndandroblnyyd-iiisnsnoattmpeerrpemmeoaiitttrhttaeeennnrcttee.nwmTthihtaeyeyn.ibnNtethEeeir-nypchloaeanyrpnepbenceettatiwtrooenaetsnnhadeanpNddpiENseaaEoprsr-piannetado2ri.ino9ttn,oAlayintNo.dnEIcotepmi.seancyloibfseetdhc-eolrouesteadorreifotpnheoinnthgiinsn,gwifhgsioocehms egootuhtoinuogtf ooorrf tiatnhhtciiionnrenggasosoeofrntihnltyheaigNnmogEosi.unAotnontnliuytNn;Egtiinolistwohcuheltoiycshobefdrci-ainitsng;eoaitnrbhooewputhethniitc-nhhogeu(ctdsa)eisfgemesonitgmhehries-t mtbcFhoooanitrnyhtgiinnatshuslbsteeoarssinencucgocneasntstiraeilebnsdtouhtuehbetelufotugnhoantdeiiclndtciteoeohglrnelesilnnoleiosgnrssasooatffiootfhsnhoytemphofieNesrtEtthtohheniiinsNincgdgEioo.sorrr(,eegdsoines-. ttjooorntiaitcly;mtohfeidsNiwuEmosu)wl.doOuinpldefnabcnetesbpseairsatnisapoltleycniaoeclpecesanss,aerp,ilesyrinmacbietsttoihlnuegtmethoaerpdlctihaaeknissencslogryainsgbtleiehyndoagftgaoseoboninnomelvryoeearltow.honouiAenutlg,ltldshwtiihainntleg/hsoocotuabhrsteeeabsNeusxaEtmtbrnobaeovmletleinenomgtuchmaaoesyprbesesae.n,rlsTsiooinhnf/bectoeehcuairitntestggeiosssubasleaidtteisrdeccointnevdtehnbeiyesnetchnees.eNtEhabtetchoemoinpgenitneospseonrincloosrecnleosssedcainn epnetni2dt.ie1ens0tfAoNrNEsEos mmiseadtyhepinbegen;ddoeetnphteewnrwdheiesnnetiittorniesqoiunthidreeerps eoennndteietoniret.smDfoorere-,
adcomenvoestnloagpnomtltyheneort.rthiTninhtegersym, ecixattinsetnaetnllsyco,e,btofeutnadlcilrtyeiocontrl,yfpooarrrmtiianatdlilioyrn,ecaatnnlydd,
moodnreoppnoeaotnhr-dteoeronrfecmneit.tu,iltItoitierpcslaaefnl-otderaerltpnshoaeentcedwheabhnneottg.lweeAeioetfnNs idEtdseepcpsaepennandndbeeenoncfdceeeepxtaoiesnnotddetnheincneetr-
NwfehEreiscn,htieannnttihetneietsist,eynwsgietivhtehstahrteiseevrtosotluoetnniotenitoymr cmeoanontrsienaunienpwgroatcnoedsesxdibisfyt-
tdpehvereoorslduteuontcoitoeidrnee.ixntaiacmtllectohsppeiaeansbooovff etthhceaemspessreotlvcheeassts..eAnItstitisitehsiosuailrnde oabrbeglaeunntioc-
omfaiytAscevoxanirtsiitanetunieocenuaunlnteidnl ettrihtgyeoeidssisaoanppeprotehcaearsatsnfocreof mvoafrtithaheteiboeenng,tiwintnyhiincohgr
enwnohdtiTcubhhneemfdoreearreygaoribtee.seuAndctehivnteoiaelnosp-pwvrmoahcreiiecnashttsai.aolrndeaudlreeivnnegtliotsypommiseeonsntpaeal-tnvhaoarftiatdhtoieoeinsr al,
and/or weight,
natuimoSnboeminr,eveeatnrcit.oituoifsestchoceomueblxdiinsuatitnnidogenresgl.eomdeenvtesl.opment and vari-
mneea2dn.1sin2to3N.6uE)ns.dSmertagayoticbaiescodtnoytnirnaeummoaiucisanlcwhoiratnhsgoteautt(iccc.hhaanDnggyeen.aismdiec-s aonwocnno2-ns.a1teicl3nft-uidAooenufssos,erlomfl-rikdindeegifsoacNrnomEnaitnmliingkoueeNobauEass;tdiostenhfoeoen.rmecoawntthiroiacnrhythuwrnoidlulegrbhgeoietass iaCtnodc-2oc, o.n1intn4afoianIrncmsc, oeaadrcd.cNaoInrEtdcesamenewcameyitshwbteihtthahdteenttnhhoueemmminnbuiaenmrtiembdoefurEmcloo-fmcnouepnmloefomnbreemenrnteotsdsf, kNmapiEnepndltmisessaobyfteoetbwlteehemecenoennmu1tspmaotbnsheedadrtnooa,ff wcNaohnEmyerpcenoaunnnmenihbstaesvr.enoTiiftshek.eoinnnTdeu;hsmetobhfseuaresmloeae-f mNttphoaEeeramtNniicbsyEleefrsoisnsrwoimfthfoeeirecdmnahucoehmbdfykbooidenfnreldm;ywnoooifritnteeiheoltenhtmkhawieennondeuotxnlovcdefaeoprkeintlieienlsoymdnfhreoooanfmvfte,eeltleooewmnrmoeeo,enmnnitfte,eat,muhripye-f bftroeormCoof1-c-oEonnll-yfcooornmnfeoedrkm.ineddotfoenle-mEle-ncto.nfTohrmereedfowreitNhEtshecasnambee Acknowledgements TVMloah.l-VelWei-aeM.yurHteahnood,aronMzdwa.o,,oaedKrrwt.aoiMnfto,harRnatn.ghikGnei,,rsAkeinni.nstH,,s aHLoln.l.idPDtahoeye-l, wnanihcyoallreeampssaaipsitnearinn,cgaelssThoohtreotycCosmh. oLiunimlgd.ancootfhoorwheisveirnvbaelubalabmleetdecfhor- References [1] Anderson C., 2001. \The extended organism." Com- plexity 6, 58{59. [2] Allen T.F.H., Hoekstra T.W., 1992. \Toward a Unied Ecology." Columbia University Press, New York. [3] Barabasi A.-L., 2003. \Linked. The New Science of Network." Perseus Publishing, Massachusetts. [4] Barabasi A.-L., Bonabeau E., 2003. \Scale-Free net- works." Scientic American, 288, 50-59. [5] Caws P., 1988. \Structuralism: The art of the intelligible. Humanities." International Press, New Jersey. [6] Eibl-Eibesfeldt I., 1974. \Etologia." Ediciones Omega, Barcelona. [7] Ezzell C., 2002. \Proteins rule." Scientic American, 286, 26{33. [8] Feinberg G., 1987. \Claves ciertas." Salvat Editores, Barcelona. [9] Fontana W., Buss L. W., 1994. \The arrival of the ttest: Toward a theory of biological organization." Bull. Math. Biol., 56, 1{64.
[10] Fontana W., Buss L. W., 1996. \The barrier of objects: From dynamical systems to bounded organizations." In: Casti J., Karlqvist A. (Eds.), \Boundaries and Bariers." Addison-Wesley, pp. 56{116. [11] Horava P., Witten E., 1996a. \Eleven -dimensional supergravity on a manifold with boundary." nuclear physics, B475, 94{114. [12] Horava P., Witten E., 1996b. \Heterotic and type I string dynamics from eleven dimensions." Nuclear Physics, B460, 506{532. [13] Horgan J., 1990. \Universal Truths." Scientic Amer- ican, 263, 74{83. [14] Huang S., Ingber D., 2000. \Shape-dependent control of cell growth, dierentiation, and apoptosis: Switching between attractors in cell regulatory networks." Exper- imental Cell Research, 261, 91{103. [15] Ingber D., 1998. \The architecture of life." Scientic American, 278, 30{45. [16] Ingber D., 2000. \The origin of cellular life." BioEssays, 22, 1160{1170. [17] Jacobs M.I., 1996. \Working Knowledge." Scientic American, 274, 96. [18] Khoury J., Ovrut B. A., Steinhardt P. J., Turok N., 2002. \The ekpyrotic universe: Colliding branes and the origin of the hot big bang." Phys. Rev., D65 [19] Klibanov A.M., 1995. \What is remembered and why?" Nature, 374, 596. [20] Klir G.J., 1993. \Systems science: A guided tour." Journal of biological systems, 1, 27{58. [21] Margalef R., 1972. \Homage to Evelyn Hutchinson, or why there is an upper limit to diversity." In: Deevey E. S. (Ed.), \Growth by Interssusception: Ecological Essays in Honor to G. Evelyn Hutchinson." Trans. Conn. Acad. Sci., 44, Connecticut, pp. 213{235. [22] Piaget J., 1968. \Structuralism." Harper Torchbooks. Harper & Row Publishers, New York. [23] Snelson K., 2001. \Portrait of an atom." From an exhibition booklet, 1-2. [24] Steinhardt P. J., Turok N., 2002. \The cyclic universe: An informal introduction." astro-ph/0204479. [25] Strogatz S. H., 2001. \Exploring complex networks." Nature, 410, 268{276. [26] Taubes G., 1996. \Rare sightings beguile physicists." Science 272, 474{476. [27] Watts D. J., Strogatz S. H., 1998. \Collective dynamics of `small world' networks." Nature, 393, 440{442. [28] Wayt Gibbs W., 2001. \Cybernetic cells." Scientic American, 265, 43{47. [29] Webster G., 1989. \Structuralism and Darwinism: Concepts for the study of form." In: Goodwin, B., Sibatani, A., Webster, G. (Eds.), \Dynamic Structures in Biology." Edinburgh University Press, Edinburgh, pp. 1{15. [30] Walter Cabrera-Febola, Spacetime & Substance, 5, 1, 34{41 (2004).
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 72{74 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
DIONIC THEORY OF MESON V.R. Terrovere1 Laboratory of an Applied Mathematics, Perm State University, 15, Bakireva Str., Perm 614600, Russia Received June 8, 2004 Dynamical properties of Meson gave way to the experimental Exploration. But a meson's Structure isn't decoded for the present, although a theory predicts that it consists of two Quarks. It is remarkable that Meson's Quarks need not endow with three Colours. Author identied a Quark with only Colour with the Dion. It is a particle that has an electric & magnetic Charge. The oered Theory permits to calculate a mass of the fundamental Quark and to calculate Masses of the well-known Quarks on the Basis of experimental Data for Masses of Mesons. It is showed that a formula for the Hadron's Mass is equivalent to a Condition of the Quantization of Dirac's Monopole. KEY WORDS: particle, quark, dion, monopole, meson, relativity
"Never to speak more exactly than You think." Niels Bohr
1. Introduction According to author a Meson is a revolving two-quark's Structure. An every Quark lives in the cylindrical world aanQduhairskspweietdh itsheeqDuaiolnt.o Ict aislwaayPsa.rtAiculethtohraitdehnatsiaens eMleacgtnriecti&c mmoangonpeotilceCdohanrogte eqxiasnt dinQth. eAnQatuuarrakl Satnadtei.ts
2. Positrony in a Field of Meson
H~ = Q~r=r3:
TheDreifaomreetEerlescQtronsQaraenidnea CeonasrteanetquMaal gannedtipcaraelldlel.
Hz = Q=R2:
A Circular Speed of Larmor's precession is equal to
v' = eRHz=cme:
An angular Momentum of Electron is equal to
M' = mev'R
1E-mail: [email protected]
or taking into account (1) and (2)
M' = eQ=c:
A geometry of Helmholtz's coil only permits to turn oAuCt oanMditoimonenotfutmhe aMn'gutlahratMdoomesenntoutmdqeupaenntdizfartoimon fRor. Electron has a shape
eQ=c = n~=2
Q = en=2e:
P. Dirac [2] obtain this Result rst. Any type of the Charge may be noted in a Measurement gram=sec [3]. Tanheanir Q mQQ; e me and a Formula (4) assumes
mQQ = nme=2e:
SaroemDeiPonasr.ticles are given in the Tab. 1. Their Quarks
3. Quantization of Quark
ICfoandsiptieoend ooffthMeesaonnguilsarvzMo=m0enttuhmenqvu'an=tizactioanndfoar Quark assumes an air
mQ cR = ~=2
Table 1: Some Particles Meson n mexp, MeV mcalc, MeV mcalc=mexp

4 139.57 140.05 1.00345
K 14 493.67 490.20 0.99296
22 769.00 770.31 1.00170
D 53 1869.00 1855.74 0.99291
Ds 56 1969.00 1960.78 0.99583
B 151 5279.00 5287.12 1.00154

3 105.66 105.04 0.99413
+ 34 1189.00 1190.00 1.00084
34 1197.00 1190.00 0.99415
as Quark may exist in the fundamental State n = 1 only. We can prove with the held of the Uncertainty relation p R = ~=2 tRrhelaacttaintohnneotImchpaunlgsee cpon=tinmuQocusolyf. QFuraormk tahnedUthneceRrtaadiniutys
(pn+1 pn)(Rn+1 Rn) = ~=2 we deduce
Rn+1=Rn = mn=mn+1 = 1=2:
But an Additivity of Quark's Energy
EQ = mQ c2 = ~ !Q=2
means side by side with (7) that a Mass of any Quark is equal to
mQ = m0 nQ; nQ = 1; 2; 3; : : :
In that way all Quarks may be considered Excited States of the Fundamental Quark m0.
4. Quantization of Meson
Btioyn'AsnEanloegrgyy wofitDhioCnosuQloQm bi'sseIqnutaelratcotion an interac-
Es = s~c=2R
or taking into account (6)
Es = sEQ:
An energy of the Really neutral Meson is equal to
G = 1 + s=2:
According to (5)
EQQ(n) = nEe=2e:
An Energy of the E(1) = 35:01303
mMienVim. NaloHwadwreonmu(nst=n1d)
stcthoreneosnrigdettehircaotlhfaMSttaraossnPgoufirneteSr-taaMctteeiosno0n=fsro.dmdFotihsretrheTaaaltibzwleede 1ta.ankdWe aae
Mass of d - Quark is equal to 330 MeV. Then on the
gcororduinndgstoof((1111))aGtot=al1Q:1u6a7r1k3's amnadssosf =Ha0d:r3o3n42is6 .eqAuac-l
to 30 MeV. A Mass of the Minimal Meson's & Baryon's
Quarks is equal to 15 MeV and 10 MeV respectively.
Therefore a Mass of the Minimal Quark is equal to 5
MeV. Further we consider that a Mass of u - Quark is
ereqaulaizletdo. 3T3h5eMn eoVn.tLheetgaroPuunrdesSotaft(e11o)f MitsesMonas!s i=s euquuaisl
5. Dynamixs of Quark IrfevaolMuteiosonni'ss eSqpueaeldtovz 6= 0 then a Speed of Quark's v' = c= ; = (1 z2) 1=2; z = vz=c
V.R. Terrovere
Table 2: The Results of the Calculation Quark nQ mQcalc, GeV Meson mQcaQlc, GeV mQexQp, GeV mQcaQlc=mQexQp
d 66 0.330 0 = uu 0.770 0.769 0.0017
u 67 0.335 ! = dd 0.782 0.783 0.9987
s 87 0.435 = ss 1.015 1.019 0.9961
c 265 1.325 J= = cc 3.093 3.097 0.9987
b 811 4.055
= bb 9.465 9.460 1.0005
and taking into a account (6)
m = ~=2Rv'
m( ) = mQ:
A Secret of the Corpuscular - wave dualism of Quarks consist in Formulas
z = vzT = 2=kz; T ! = 2:
According to (14)
E(z) = EQ = ~ !Q2 = !(z):
This result diers from the de Broglie's equation
E(z) = ~ !:
A longitudinal Impulse of Quark is equal to
pz = m(z) vz = ~=kzR2:
tionThis Result also diers from the de Broglie's equa-
pz = ~ kz:
From (16) and (18) this Formula follows
E2(z) = m2Q c4 + p2z c2:
It is remarkable that for a Deduction of the given Fhoowrmiutlhaaist hwaapspneontedbeasuaseRtuhlee!SeScinonced Newtonian Law
v' = 2R=T;
m(z) = ~T=2R2:
Therefore this "Mass" is proportional to a Period of QuaFrokr'ms Ruleavso(l6u)t,io(n8)Ta.nd (21) determine an essentially dierent Sense of the Mass's Concept and a Mechanism of the Mass's Creation. According to (8) the mass is a
measure of Quark's Rotation. According to (6) it is possible a Quantum Creation of the Mass by the Quantum Reduction of the Radius R. It is necessary to expend an Energy for a deceleration of Quark's revolution ! tthoattutron iancVreeacsteora oSfpeQeudarvkz'.s PImrapctuilcsaelliynitaiCs ynleicnedsrsiacrayl wpaorreldnt'Rs l.ikAe na FinornceiteolfyQSumarakll'stuInrnertoifa tahnisd Vsoecwtoermaapycall a Quark's mass by the Inert mass. But not in the least it is evident that this mass is a Gravitational Mass since a vexed Question is open. Does a meson generate a Gravitational Field really? Author is not assured that all Elementary Particles generate a Gravity so is conventional to think.
6. Conclusion
a a
Dionic Structure New deduction of
of the Meson the quantiza-
tion's Condition of the Dirac's Monopole.
contAranrAyntaolothgeouesxFpoerrimmuelnatfaolrDthaetaH. adron's Mass is not
ditioOnnofthQeuBaraks'iss qouf atnhteizuanticoenrtaisinotbytareinlaetdi.onAthMeaCssono-f
tahlleowfuenddtaomceanltcaullaQteuaMrkaswseass ofofutnhde ewqeulla-lkntoow5nMQeuVa.rkIst
by the Experimental values of the Meson's Masses.
It is showed de Broglie's
the IQtuisardki'sscoRvoerteadtiotnhaatsitamQauyarbke'simMpalsys.a frequency of
References [1] J.P. Sartre, \L'etre et le neant." Paris, 1930. p. 13. [2] P.M. Dirac, Proc. Roy Soc., A133, 60 (1931); Phys. Rev., 71, 1, 817 (1948). [3] V.R. Terrovere. In: \Recent Problems of Field Theory 2001{2002." ed. A. V. Aminova (Kazan State University, Kazan 2003), p. 430 (in Russian).
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 75{77 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
Phon: +38 (0572) 94-98-51, Kharkiv, Ukraine Received May 26, 2004
The experimental conrmations of prognoses which were made by the author in 1992: about new, beyond gravita- tional interaction (\dark energy") by intensity 10 52 of unities of the strong; about new, a neutrino interaction by intensity 10 26 of unities of the strong; about presence at a neutrino the rest mass 10 32 g; about a substantiation of charging asymmetry of the Universe by a corollary of its masses-oscillations in coordinates \substance"|\antimatter" are given.
1. Introduction
I.R.Prigozhin: \Einstein believed that the time orien-
tation and time is illusion | the time orientation arises
when we introduce articially the time in the untimely
Universe" [1].
V.L. Ginzburg: \The future theory ..., maybe, will
bring something new, but what exactly, I do not know
(muencdhearnsicuss)p"ic[i2o]n. is the concept of time of a quantum
sinurteThmeheewnotosprp(kposhrotyufsnitcihst)ey time problem," and
pobotratainnetdctohroelleaxrpieesr,iminecnlutadlincognsurcmhawtihoincsh. have already
2. About the New Beyong Gravitational Interaction In the work [3, pp. 38{42] is reported that in 1998 aeit9chxs9ateilsr%topnepaanihpttcyueeisrrsieuchnpiosakotfvnssestoithwbdhilisenesceUnutnoesSewsrAsignt\yagadt,nieatdt,rhkitAsahteunans\toet.trr.tga.hkyleinw,aoUaiwtsbhnenoti"vurne;etlrefitscauheebrsetisshlhipitetohyyruyiloosnd-ff"tnioenrgayl e\ntehregyin,"teallbigoiubtleaanpsrwoberlemuntoifl lF4i9nig]e..Isn1Ao,1mfi9ss9oes2nrh,gioetwsthhneoesfnieneincstetehseresriieatwscytooiorofkfnisneoxtf(eikstrthaneecontwcaioenuntohasfonhtrdohu[e4eld,xcpopbmepec.ptnel3dee8tw){e, 1E-mail: [email protected]
expected the beyond gravitational interaction by the intensity 10 52 of unities of the strong with the typical for it a stable fermion with mass 10 104 g (gravitino). Indications of this new interaction took place in observations which are given in work [3]. Repeatedly this prognosis it was informed by the author also in the work [5, pp. 127{128].
3. About the New Neutrino Interaction In the work [6] have informed about the series of experiment with neutrino which have been carried out in 2001, in laboratory of Fermi (Chicago, the USA) on the most powerful accelerator of particles. Experiment have given the unexpected results: diversions of the experimentcaolmdeattao fcroonmcluesxipoenctaebdouwterneecseossgirtyeaot,f tehxaistternesceearocfhtehrse new, unknown force which act on a neutrino. In 1992, in work [4, pp. 38{49] the necessity of existence the new neutrino interactions by intensity 10 26 of unities of the strong, the typical for a neutrino, with a predicted rest mass 10 32 g, Fig. 1 also was predicted. Conrmation of necessity of a rest mass at a neutrino has been obtained in 1998, in the work [7, p. 34].
4. About the New Overstrong Interaction
The third predicted in 1992, in the work [4] new over-
1013 of unities of the a dotted line), should
I.M. Galitsky
Figure 1:
arise (\switch on") as a corollary of the further devel-
o[4p,mpepn.t4(2e{x4p5a].nsion) of the Universe in 1010 years,
The typical stable fermion for this interaction is
ttlihhnereo)su.tgahblefe1r0m10ioynearsm, 0Fi=g.
24 g also shown by
Analytical dependence of rest masses of the com-
plete lines of stable fermions (known and expected) and
the views of interactions relevant to them (also known
and expected) from Fig. 1 will be determined as
n = jmynn j ;
mn = mmin < m < m < me < mp < m0 (2)
yn = 0:50; 0:91; 0:81; 0; 0:48:
Value of the gramme):
mn = 10 104 < 10 43 < 10 32 < 10 27 <
< 1:7 10 24 < 2:7 10 24
wdtheherenstthcreeontfohgre)m:cuolmap(l1e)tewsiellribese odfetveiremwsinoefdinatser(aincttieornms suno-f
n = 10 52 < 10 39 < 10 26 < 10 13 <
< 100 < 1013:
stabIlne tfheermfoiormnsualansd(1th),e(e2x),pe(4ct)eadnvdieownsFoifg.in1teerxapcetciotends rpelleetSveaelqninuteetsnotoitfahlveimfeowramsroeaftuiionnntdee(rr\alscinwtieiodtnc.hsi(n4g) aonnd")thoef cthome cpolemte-
Figure 2:
lines of stable fermions (1), (2) relevant to them, happens when the Universe is dilated, and the furl (\switching o") happens when the Universe is squeezed,ig. 1, 2. (Electromagnetic interaction is considered as uniform electrofeeble by intensity 10 13 of unities of the strong). Fig.T1hceanviseewrv(ebbeyauotnye, msiomreplaicrgituym) eonftt(hbeesfiduensctailorneadony obtained experimental conrmations) for the benet of its reliability.
5. About the Solution of the Problem of Charging Asymmetry of the Universe (\Substance" | \Antimatter")
Really apparent parameters of the Universe are well in
accord with its radius of SHvartsshild
2 muniv: c2


wthheeIrUnentimhvieusrnsicveo:,n ne1ics0ti5ao7nst,gattihsioetnhUaernycivovemarlspueleestohefomgurlaadsvsbi-teeantceioorgnnys.ido-f ered as quantum object (\a black hole") with new effect of masses-oscillations proper in it, Fig. 2, [4, pp. 51{54], [5, pp. 128{129], in coordinates \substance"{ \antimatter" with frequency
10 muniv: 57 Hz;
wtFhihege.nU2c)eniwvthielrelsmepea(rkfioeord eoxfaomnpelea,ctinofampahssaesse-o\scsiullbasttiaonncseo,"f
= ( ) tuniv: muniv: 1 1057 sec 1050 years: (7)
sitioHnenfrcoem, foar sta1te05\0suyebasrtsantchee"Uinniv\earnsteimreaatltizeers" t(raanndon the contrary), than the problem of charging asymmetry of the Universe is solved: at the given stage of development it is in a phase \substance" (on Fig. 2 it is shown as \a current state of the Universe"). In transition points (singularities) 0, 2, 4 on Fig. 2 impulse of the Universe will make
P univ: =
! 2
cos '
vuniv: c
from this follows that in these transition points the Uni-
verse with velocity, to the close to light, \fails" in a
singularity (points 0,2,4), \by-passing" it in area of the
negative (positive) values as the relativistic impulse of
the Universe (8) excludes other opportunity of develop-
ment of events, Fig. 2.
6. Conclusions Vtino.cLo.mnGdpilanetzelbintuetrlsges:ainn\fdo.rn.m.oteadcllropesahudyryseictsshimewfphulinycdhiatmwioseuniltmdalpntoohstesoisbreylee, .pl.ah.tyenBsdeiacwacsbkpaoghnvrydoesufiincnosdllasouswntorcfofornenomodmmbitoytiohd"ney[ai8onl]lb.gyt,aoiiftntieshdencepocmreospgsarleartyme blfioontrehms iuonfv\opcriheyoyw,ms"sicpwoslefiattinehnndtefeosirnslalcoaatwsnitoidrnnogsano(fcrkmlonoymos.uw"rhneeraoenfd\tnheexewpfeucpnthdeydas)mi,cespnrbtoaovltidhthinieng- Other new results are also obtained [4], [5].
References [1] \Scientic and Technological Revolution | Problems and Solutions," Moscow, 23, 1987. [2] \Science and Life," 12, p. 18, 1999. [3] \Science and Life," 3, pp. 38{42, 2004. [4] I.M. Galitsky, \Future of Physics, Mathematics, Sci- ence," Gomel, 1992 (in Russian). [5] I.M. Galitsky, Spacetime & Substance, 4, 3 (18), pp. 123{ 135 (2003). [6] \A planet," Leipzig, Germany, 1, 2002, p. 5. [7] \Science and Life," 2, 1998, p. 34. [8] V.L. Ginzburg, \About Physics and Astrophysics," Moscow, Nauka, 1985.
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 78{82 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
STRUCTURE OF PHOTON & LEPTON V.R. Terrovere1 Laboratory of an applied mathematics, Perm State University, 15, Bakireva Str., Perm 614600, Russia Received June 21, 2004 The present author develops a new theory of particles on the basis of fractals and clusters. The theory contains two radical suggestions. 1) Any particle is divisible without end. 2) Any charge is a power of a source. According to Author a Photon consists of Neutrino and Antineutrino. This idea has allowed to calculate a Neutrino Mass spectrum. In Author's opinion the published experimental data 2.2 eV (V.M. Lobashev a.o.) are understated since the Experimenters leave out of account |eect. According to Author electron consists of the Preons. The Mass of Preon is equal to 7.3 meV. Preons radiate Photons. A wave-length this Radiation is equal to 0.662 mm. A "Relic" Radiation has the same wave-length. Thus both euristic ideas have an Experimental corroboration. KEY WORDS: photon, lepton, preon, |eect, "relic" radiation
"If it dawned upon You then You must seize it by the use of the death grip and not let it what ever happens". W. Heisenberg
1. Introduction The present work is a continuation of the articles [1, 2tEPh]lh.eeoncAttoirutontmnhcoumorsnuthssihotslatdhvssaeovtaefhsaaNttrSeuiutfcrttauruicnPrteoua.rrateIin.ncdlpAeauAhrttanhisctoiuwrnleaasuurvtpePrpiphnoroosote.podneTrtathhinaeidsts atcsariossuMsntumstameo.snfsptettAohidfoe.nctPFhoaiuernlerlPcootihnwrdeeseso.rnntTaco.euhctAiwhasloiapctrsurhsesluaoutmtnphepephaotaEsisoNexsnaepuntaehtlrlEraiomitlnweoeEcsntltMtreoaiccatlcrsaCDoslnhcaSuatcplreoaegntceies--. Iqoidtfueaetanbhscseyoor"fboRAfsetuolhirtcih"sroaRrRdiaaaaddrteiieaasttciiPooorhnnroo.ctbooOoinnrnsac.tidteIhdetasatewpxwpipteaehayrritmebhdoeetntfhhtraaeelqtluyuareiansfrtnceiydcso they may obtain subsequent Development. 2. Global Relativystic Neutrino That is a particle which moves with a constant speed unaitnote>iuvtcthicrseiatnialcocwloyaponlyiafgnsrtd.tthirhceiWelcePaghlhoeanowottdoogcernoesldonicimdsaoietanfitdorttynhyipefdtihccohiaaerilstscuetsaxlhpaaisermspecdinpryaelleiuuln1tomdrfieionrtstohiReeolqni.ruveeoaAls-fl 1E-mail: [email protected]
nsWsstiptheoraeuhanctaicergotyi?hfnlmtiotnehSldrtieinaernirienccs.seeedWu?xoat0ereFisgnisaerahosoratemmslpolteofahbttcreaireoyilnlngigoesiotoffrediiqtsngehueshoeaiutbcltscvartyiinwoonlginuoonl.sedg,tdeAhetrnechnoeaiderst-avtotoa wreladvdotiieinnmontantthethleneoyinss-f! iappnnllaadtnnheeissa(p-nxla1ae;lnloseen)m:gtexhtn1hetea|Nrayerawctlrotoionafngntigtahhlneeecpgylealninneedr.aetrWricxeirocmfleat.hrkeWcoeyultcinatldhleiars
(dx0)2 = ds2 + (dx1)2:
ds = R d'; d' = ! dt; dx1 = c dt;
(dx0)2 = R2 d'2 + (c=!)2 d'2:
Let speeds
speeds of own neutrino are of other neutrino are equal
equal to u2;
to !2
(dx0)21 (c=!)21 d'2 =
= (dx0)22 (c=!)22 d'2 = R2 d'2 = inv:
Using a limit of neutrino speed, we turn out
d' = ! dt = !max d;
dx0 = u dt; dt=d = !max=!:
(1) 3. Charge
| aWreelsahtiavlel cMalilnkowanskai btismoleu.teTNheeswettoinmiaens atriembeinanddbyt ratio u2 dt2 (c dt)2 = c2 d2:
AeleNcteruotdryinnoammicoduenliotsf pofhomtoenasaulrleowasndtotroefcuosme efrotomnaontehleicntgromdyonreamthiecnEbnaesrigcyuDnietnssoitfymeasure m; sec; kg. An
Hence it follows dt = d; ! = !max= ; = (2 1) 1=2; = u =c:
W = ("0=8)(E2 + H2)
is identied with a Kinetic Energy Density of the rota-
tory movement of Neutrino and Antineutrino
We shall consider our space dx1 real quantity. Then hence it follows that an interval ds is an imaginary
W' = 0:5 0 v2':
According to (9) and (10)
(i ds)2 = (i dx0)2 + (dx1)2:
0 = "0=2 andA[nE]el=ectmri=cs;force is["e0q]u=al ktog=m3.



0 :
oaSdderwincNTsaaevleeauwo-ntfordltrienhlnbdoegyitIdnthnohtweaeshrtv.ioocawhnlInen\Slgriteovihvseeeossa"lpauctrtidheirosiecsenltnpeatrS-nelcsce=eeannsgx2ett1hnaetoRuhgftaertoitihnmniesoae.cetpyrqIiletucirnaaiis--ll evident that
u1 = x1=t = =T:
aun1d.LToetthheoenwr onnnenutethureitnrgoinrmoouomnvdoessve(ws4i)wthitphapraamraemteertsers2;T12;;Tu12;
u1 <

u1 T1 1



u2 T2 2
F = qE:
From Ionf
of time. This conclusion has a fundamental mean-
i11ttdnhi0ivkgeeg!u1R=Ss5siaoIog.dnun=irTcacEtmtehhiqeoe3iuns;naacat"dhir0ooaenp=nstgt0eae8da=t:8ibou5l1nen4:.a4itr0I1y9to0sofmr11m02caChet1aah25ns=eumgg(rN=eeaactmbi1lcme3aC..2l )AomSu=oorluoadr8mdec:li8ebosi5as4o=ca-f
@ @t

matAheCmhaatricgael ims oadeplroispaenrtyEqoufaStitoantionary Source. Its
= (1 2) = (1 1 2):
We call a plane (x0; x1) a real plane of Minkowski.
According to (3) its metric is the pseudo - Euclidean
(i ds)2 = g dx dx;
g =
we Bshyaallnbalroinggy waitshpeaedve-vcteocrto(rx0(;vx01;)v1o)f.thWe weocraldll-poowinnt-
component speed v1 = dx1=d a Newtonian speed. We
cspaleledtw. oW-ceomshpaollnceanltcuslpaeteedanuin=vardiaxnt=dvt
a v
v0 = u; v1 = c; v = gv:
The speed v0 is absent in a Newtonian Mechanics!
vv = c2:
A physical Sense of this Invariant is that a speed othfethceonNsteruatirninedo Niseeuqturianloc. always under a denition
@ @t

= f(~r) T(t):
T0(t) = i T;
@ @t
i :
VoluIfmVeeoifsEaleVctorlounm, ethoefntihtes and
for example equal to me
is a Ve
@me @t
i me:
itno tAheSSotuartceeooffPthheotEolnesc.trTomheargenfoerteicitFsieCldhalorgseesisa eMquasasl

@me @t


V.R. Terrovere
mthaesIesnlteotmhweantitthwairanyyaPafaurCnthidcaalermgseeisnotefaqltuhcaoelnStsootauunrntciet yis.inAeqauCnahelaletrocgterhoois-f dMtoyansasm. Tichuenreitfooref ManeaEsnuerregyanodf tdhoeeisrni'nttedreapcetniodnoisnetqhueairl
U = e2(m1)=r = e2(m2)=r:
But in the mechanical unit of measure
U = Q21=4"1r = Q22=4"2r:
Hence it appears taking into account (11) and (16)
"2="1 = (m2=m1)2:
4. Mass of Neutrino
shaApeCondition of the quantization for Photon has a
m c = h:
An Impulse of Photon is equal to
p1 = ~k; k = 2=:
Taking into account (2) and (5)
m = h=T c2 = ~!=c2 = mm ax=m : Therefore
E' = ~! = m c2; p1 = E'=c:
Let an electromagnetic wave consists of Photons and a distance between Photons is equal to the wave-length on.e TPhheontoan feuxnadctalmy.enItnalthRaetgcioanse Va m=assRo2fPchoonttoaniniss equal to
m = 2m1 = 0V:
For the Then
V1 = 22R3; R = ~=m1c; m1 = 2(~=m1c)30:
Taking into account (11)
m1 = p4 ("0=2)(~=c)3:
um.InTiatki"n0giisnaacpceorumnitti(v1it9y) oafFeolercmtruolan-(p2o4s)itirsongeVnearcaul-ized to all types of Neutrino
mL = p4 ("0=2)(mL=me)2(~=c)3; L = e; ; : (25) ble T1.he Results of the Calculation are given in the Ta-
Table 1: The Results of the Calculation Neutrino e, eV , eV , keV According to (25) 15.635 224.83 0.92387 According to [3] < 17 < 270 < 35000
A value of The contained inside
tMheasdsiaopfaEsolenctorof nthNeeeuxtprienroimmencntaualecl
erroneously. He leaves out of account that - eect
may be takes place in his "new" - spectrometer.
- eect [6,7] is an induction of the electromotive force
E~ = B~ which has a direction of the magnetic field
B~ for the left Electron and an opposite direction for
the right Electron. Electrons obtain an extra Energy
E(B) at the expense of - eect in - spectrometer
[5]. Therefore it was found that a registered Energy of
Electron is equal to
Eeexp(+B) = Ee + E: If a Direction of B will be opposite it will be found that
( Eeexp B) = Ee E:
equIanl ttohat way true value of the Electron self-energy is
Eeexp = 0:5 (Eeexp(+B) + ( Eeexp B)): If - eect exists really then an Experiment will gtoivethae fEunxcpteiroinmaelndtep[4e]ndmeonscte omf eaxelpl(Bbe)c.auAsuethitordotreusnst'st have -eect.
5. Electron
AAItcSococtrcruudcpintiuegsrteothoAef utVhtohelouermleacentreolenctisrotnheconnsi-stsstroaftuthme PSprehoenres..
Vn = (4=3)(nR)3
A free will of each Preon is limited to the Volume
V1 = (4=3)R3
Formulas (26) and (27) permit to calculate a NumbNviesoNrusoisnfiLnPtahtryheeeoern.SesuAxrtNfeDarVcneeapilneLnLaVdayeoyenlerucrmeainnoedfcVottnhmhe,epsaeaIrNnqiscuuoramennabtwsieetiritehoosfftihsPPegrreeipvoorennenssin the Table 2.
Table 2: A Dependence of Quantities n 12 34 5 6 NV 1 8 27 64 125 216 Ns 1 7 19 37 61 91 Ns +6 +12 +18 +24 +30
Ns=NV = fV =fs:
tahllePAErleceohcntarsrognieniostfheoeqnuceaelnPttroeeroQnoNfiEs=leeqNcutVraolQnt1ot.hQIefn1w.aeAnshCEanhllearlroggcyeatooeff their Interaction with every Preon of the Surface Layer shall be equal to
U = NV Q1 Q1=4"0Rn:
Since V = U then
fV = Q21=4"0Rn:
Any Preon absorbs or radiates one Photon only. A Surface Preon radiates Photon with the Energy fs =
fs = ~!:
Ns=NV = Q21=(4"0Rn~!):
ttraolnRc.oanItstiotamNnetsa=tnNosoVt.hiaWstaeafusQunpdupaaomnsteeintyttha!al tcRoannsStipsaneaetdFofuotnfhdPearEmeloeenncs-revolution in the Surface Layer is Highest possible i.e. V' = !Rn = c. Then
Ns=NV = Q21=(4"0~c):
In electrodynamic units of measure
Ns=NV = e2=~c = :
preoAnsFionrmthuelaE(le3c2t)ropne.rmits to calculate a Number of
Ns = (n + 1)3 n3; NV = n3;
Nn s==N[1V=(=p3 (11++nexp1)3
1 1)]:
A mAacscsoordf iPnrgeoton (is33e)qunal=to412; NV = 69:934528 106:
mpr = me=NV ;
mpr = 511 keV =69:93428 106 = 7:30 meV: (34)
6. Background Radiation
According to the oered Theory all charged particles are pulsating Sources. On the ground of (16) a frequency of Pulsations is identical for all Sources and it is a fundamental Constant . It is possible an Existence of the Constrained Structures of Microparticles and a Thermodynamic Equilibrium of Universe on condition that a reradiation of Sources is eternal only. A wcaalvcue-llaetnegotnh tohfetghreoubnadckogfrtohuenfdolRloawdiinagtiCononspidrermataiyonbse. According to (25)
= me=mpr pNV :
Since me =mpr = ! e =! pr = pr = e , then
= pr e pNV :
For a virtual Neutrino v' = c: Therefore
= 2 = e Re; Re ~=mec:
me = 15:635eV=5:61 1032ev=g = 2:787 10 32 g;
Re = 0:3515 10 37 g cm=2:787 10 32g =
= 1:26 10 6 cm;
e = 7:917 10 6 cm; pr = 7:917 10 6cm 8:363 103 = 0:0662 cm: tal dGiaivpeansovnaloufethe pwr aivsec-olenntgatihneodf tinhseid"eRtehliec"exRpaedriimateionn0:25 0:059 cm. Since a background Radiation is eternal then it isn't logical at all to explain a origin of the Background radiation by means of the Big Bang theory.
7. Conclusion An assumption about the Neutrino Structure of the Photon allowed to calculate a Spectrum of the Masses otdhfaetNoaree[ut5ti]craianlroev.aulunEedxepmresrtciaaemltcee.dntIsanilnmcdeaytVao.pM[i4n].ioLmnoebExeapxsphceeorvnimleremanvteaasl out of account an increase of the Electron Energy in -spectrometer at the expense of the -eect. virtuAanl EPlheocttroincsalaCndhatrhgee Cishiadregnetihaeds twhiethUaniCtumrreeanstuoref kg=s. An Assumption about a Preonic Structure of the Electron allowed to calculate a Mass of Preon and a frequency which a Radiated Background Photons have. Tquheinscfireesquoefntchye i"sRcoelnitca"inReaddiinastiidone.the experimental fre-
Acknowledgements The Author thanks P.M. Simonov for the computer service.
[1] Vht.tRp.//Tseprarcoevteirme,e.Snpaarcoedt.irmu.e & Substance, 1, (2004),
[2] Vht.tRp.//Tseprarcoevteirme,e.Snpaarcoedt.irmu.e & Substance, 1, (2004),
[3] T.P. Amineva, L.I. Sarycheva, \Fundamental IntUeRraScSti,o1n9s99an(dinCRoussmsiiacnR).ays." Moscow: Editorial.
V.A. 1177
Lubimov (1961) (in
[5] V14.M(2.0L0o3v)a(sihneRv,uBshuilalent)i.n of Russian Acad. Sci., 73,
M. Steenbeck, (1966).
[7] R.M. Steenbeck, I.M. Kirko, A. Gailitis. Monats D.T. Acad. Wiss. 9, 716, 1967.
V.R. Terrovere
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 83{84 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
Institute of Nuclear Physics, Uzbekistan Academy of Sciences, Tashkent, 702132 Ulugbek, Uzbekistan Received July 27, 2004
Both electron and its neutrino possess not only the anomalous magnetic moment but each of existing types of the electric charges and their dipole moments. Any of them can interact with eld of emission leading to the elastic scattering on a spinless nucleus. We list some implications implied from the analysis of these phenomena in the case of one - photon exchange. The processes cross sections give the possibility to establish the individual as well as the united equation between the Dirac and the Pauli form factors of light leptons. They dene the electronic neutrino electric charge as a consequence of the availability of a kind of mass.
In many works a question about the neutrino with a non - zero rest mass was investigated. Analysis of existing experiments assumed [1] that a massive Dirac neutrino must have not only the magnetic moment [2] but also the electric charge. Such a conclusion one can make by following the behavior of the neutrino in the nucleus eld. From this point of view, the spin phenomena [3] may become highly useful. In a given work the elastic scattering of electrons and their neutrinos on a spinless nucleus have been considered at the account of fermions charge and magnetic moment interactions with eld of emission of virtual photons. Starting from the processes cross sections equality for longitudinal polarized and unpolarized particles, it is shown that if the neutrino corresponds to the efaleccttorrosnof(th=e nee)u;tbrientoweaenndtehleecDtrioranctahnedretheexiPstasutlihfeorinmdividual as well as the united dependence. They state that the four - component neutrino possesses both normal and anomalous electric charges. Herewith its full electric charge has the size
e = 34eG2Fpm22 ; e = jej:
Such a regularity, however, meets with many prob-
lems which give the possibility to make the most diverse
predictions. The treatment of any of them would bring
us too far and all they therefore will require the more
detailed description. But here we can add the following.
Using (1) for the eV and taking into 5 GeV 2; we nd
e = 6:267 10 25 1meV2 e = 6:27 10 23 e: (2)
in nEeaurtlrieornladbeocaraytodreynfaecttshaenudpcpoenrselirmvaittio[6n] oefqcuhaalrgtoe
1E-mail: [email protected]
echarsccoantctleurdineg[1e]xtpheartimeen[1c70o] nas2si1sdueemr: aAetdinoan[8lsy] sftoishraottfheeelansecharWgee lreeacdogtnoiztheetehsattim(2a)tev[i9o]laotfeesthvation law. There are many uncertainties both in the
nature and in the size of the neutrino mass. Another
reason of inconsistency is the absence of quality picture
otehsftaatble-isdhp2r1oceestsheesn. tNaekvienrgth(e1l)e,sist, iisf theoretical bound on the
nwoetsduippcouslet [t1o] neutrino mass:
mthe BivtalwuHaeasivnfion(ug1n)dtghi[ev1e1fs]ortemhauthis fact
that the force of the Newton attraction between the
two neutrinos is less than the force of their Coulomb
repulsion, we get the following estimates of
me>>4433G2G2pFpF22GGNN1e==2 =1:14:6531010303ee;V;
(3) (4)
wheOref cGoNursies,tshuechcoansdteanntiotifognraovfivtaaltuioensaolfe(m3)isasinodn.(4) is not very standard. At the same time the existing laboratory bounds may serve as further conrmations of our earlier ndings. Insofar as the discrepancy is concerned, it re ects just many properties of a certain latent regularity of general picture of massive neutrinos. In the framework of the loop phenomena, the neutrino must be electrically neutral [12] at the condition of gauge invariance. It appears that here on the basis of
84 (ta1hn)eoonnneue-tcrzaiennroowpiinhlltyedsrieaccacitdliemonaasqosfutePosatziueorlnio.aarbBisoueutstwatethectahenequseaaxylpitetyhnasoetf onagfsaeuuautgnsreuiinaninlodvDiiacniarrittaaihconencienlto.tooetrphacaetpnipoenrwo.xsTitmrhuauctsti,uortnehoeonfneeelmuecturtsartolimtinyategornfpetrtheiect References [1] S. Davidson, B. Campbell and K.D. Bailey, Phys. RSuenvd. aDresa4n3,, J2.3P14hy(s1.9G912);0,I.1S7.4B9 a(t1k9i9n4)a.nd M.K. [2] K96.3F(u1j9ik8a0w).a and R.E. Shrock, Phys. Rev. Lett. 45, [3] RM.aSt.hS. hTaerhan.dEdsinteosvt,. D7,o2k5l.(A19k9a8d).. Nauk Ruz. Ser. [4] R(1.9G9.1H).. Robertson et al., Phys. Rev. Lett. 67, 957, [5] G. Bardin et al., Phys. Lett. B 137, 135 (1984). [6] J. Bernstein, M. Ruderman and G. Feinberg, Phys. Rev. 132, 1227 (1963). [7] HLe.Stt..G2u8r,r1,4F0.6R(1ei9n7e2s).and H.W. Sobel, Phys. Rev. [8] A.P. Rekalo, Ukrain. Fiz. Zh. 18, 213 (1973). [9] J. Panman, in Proc. Int. Symp. on Lepton and P19h8o7to(nNoInrtthe-rHacotliloannsd,aAt mHsigtehrdEanmer,g1i9es8,7)H, apm.5b5u3rg, [10] V(1.9A8.0)L. yubimov et al., Phys. Lett. B 94, 266 [11] KSo.koElnoqv, iPsth,ysV. .ReSve.mDiko4z8,, 4A5.57Sh(1u9k9u3r)o.v and D. [12] J.L. Lucio Martinez, A. Rosado and A. Zepeda, Phys. Rev. D 29, 1539 (1984).
Rasulkhozha S. Sharaddinov
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 85{86 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
Kharkiv, Ukraine Received May 26, 2004
Multiplicities of masses, time (frequencies), the dimensional parameters were considered in the previous paper \Multiplicities of fundamental physical constants. Cosmological model". The deduction is obtained that a continuum { space { time { eld { substance are structured. Correlation of a series of multiplicities has enabled to interpret, the obtained results, as cosmological model. It has been put forward a series of theses. One of theses treated a compendency of parameters of space, time and a multiplicity of masses, as structurization of space { time { substances (empty space { elds { substances). It is a corollary of existence of a uniform, quantized continuum at all levels which has blanket laws of the organization, and as a whole, with the mechanism of regulation of processes forms a blanket Universum.
1. The frequency relations
In the previous work the multiplicities of frequencies (time) 1020 in a range from Planck frequency up to Hubble constant and a probable life time of a proton 1037were considered: T (s) 1038101810 210 2210 42 or 1037101710 310 2310 43:
Figure 1: A scale of time { frequencies.
1 2
Hubble constant is really dened quantity from astronomical observations, and the frequency 103 Hz is measured, but with this frequency known physical effects, except for frequency of a sound range are not bound or not interpreted. lengAthboouftdteheBCroojml pfotronafprerqoutoenn,cyitfips rpeolesvsiabnltettooaswpeaavke in correlation with existing experimental data on denition of radius of a proton
r = 10 15m:
rPeltainPcaclklanqfcurkeaqnfruteieqtniuecesyn: cctyoprarinessdpnaoontpdrcsootntoonrmalifeehdtyimpexoepthetperismiasreenotfthatelhloye-. Big Bang. For this hypothesis the models and with other parameters [1] designed. In stationary models [2] it misses. Thus, Hubble constant, frequency 103 Hz which is not having physical interpretation, and Comptpohnysfirceaqluqeunacyntoitfiaesp(rFotigo.n1f)p. concern to really apparent For frequencies the relations will be fullled:
f = (f1
1 2
=1 2
1E-mail: [email protected]
2. Multiplicities of velocities
Ltheet'ms cuoltnispildeetroathseeriveesloocfitvyaloufesligohftvienlovcaitciueusmwh1i0ch8:are

m c

Values 10 32 and 10 12 have physical interpretation; values 1028 and 1048 have explicitly debatable character. Nevertheless, there are eects which can be treated with viewing velocities, reduced orders; moreover, the models of some eects have physical sense only in limits of such values. We shall consider these quantities (1). If to correlate values of velocities (1) with the multiple values of the relevant radiuses: r (R) (m): 10 35 10 15 105 1025 1045, we shall receive the following relations:
10 10
32 35
10 10
12 15
108 105
1028 1025
1048 1045
or the frequency relations:
f = (f1
1 2
=1 2
1 2
mcoorrdTAeeshlpseaeosrnenidedsrsaeotlwafaitmtihomunialsctrispotelalriekicveieestile.opsflaomcfeuglrbtaiovptilhticaittiiinoenscaoolfspmvoeotlelooncgtitiiaciealssl (1):
m r
fceorleroclatervpoemrlotathogennseeatniqcd,uamfneoetbidtleieelsoafanrfdoergmsrmaavatilioltanbtuoioftnmnaluacsilnse.taeArratfcoatricomensis,adarneera.llyinsTiksehdoefagenixvdiesnthianmvgeoctdohenelsfrrmaelqsinuogenweciylelcrbtesel.atsiuornvseyoefdsuacth tohre-
References [1] Sof.St.hSearnenlaiktoivvis\tCicosbmigoalmogilitcoanl oavspyhectosf osfysttheemtsh"e.o/ry/ I(z1v9.96V)u.zov. Physics, 38 (2), 106 (1995); 39 (8), 72 [2] Npr.oAa.chZhtouckinte\gKravtaidnrgodfiunnadmaimkaent{al tihneternaecwtionasp"-. The Kharkov International Conference \Gravitation, Cosmology and Astrophysics," Theses of reports, p. 90., 2003. [3] Gics.,"VeMjlo. c\kAowg,ro\uNpautkhae,o"ry19a8n6d. a quantum mechan-
V.F. Barybin
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 87{90 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
V.V. Balyberdin1y, A.V. Nechayev2z
yResearch and Technological Institute of Transcription, Translation and Replication, JSC, Box 589, 3 Kolomen- skaya St., Kharkiv 61166, Ukraine zNational Academy of Sciences of Ukraine. A.N. Podgorny Institute for Mechanical Engineering Problems. Kharkiv, Ukraine; Research and Technological Institute of Transcription, Translation and Replication, JSC, Box 589, 3 Kolomenskaya St., Kharkiv 61166, Ukraine Received January 3, 2004
The preliminary qualitative experimental results of the in uence investigation upon the weight of the laboratory container of thermal magnetic chemical process, made in the container, are presented in the paper.
1. Introduction In 90th years of XX century the research divisions of RPA called after Lavochkin (Chimky, Moscow region) and the A.N. Podgorny Institute for Mechanical Engineering Problems of SA in Ukraine (Kharkiv) have carried out experimental checkout of S.M. Polyakov's idea about the interrelation of magnetic and gravitational interactions on the basis of a governmental decision about the research carrying out as to the search of new physical principles of ying apparatus travel. S.M. Polyakov carried out the experiment as for a thermal destruction of magnetic rings from the cast alloy UNDK conrming the stated imaginations, in which he observed shock aect upon superstrong ceramics at the magnetization destruction in a ring structure. He identied this aect as gravitational impulse. S.M. Polyakov used microwave-radiation placing magnets to the resonator inside for prompt magnets heating above the Curie point. Despite of the arguable deductions by the experiment results, but taking into account S.M. Polyakov's theoretical imaginations logic, it was decided to check his hypothesis in a bit dierent experiment accomplishment. We have developed the experiment scheme as to direct recording of possible power eects at the thermal destruction of cast magnets and ferrite magnetization to fulll this task. 2. The idea of experiment
tfwuoismarecldlae.gnmHnoeeontaw-isgceuavvrseieenrsogsuuedsnl,elfivehkriaecrneiStget.eMo-dma.atPhgxornoeleydutaigbckhaotrvear'ssmetteeinxtinespoefarro-ilrmmatbeehoanerstausmt,roiawnrgygeniapmselatteshnhmeteaahatceiincanotgaim.nmgpAalpcigscrhnoomecrtdeiesicnnstgisertlecdopa.rorerSuisureedcnihmtoshuaiegtnaibdntyieanptlgoieownpnd-rstoeesncmuetcsphisnecteraexarntpeuesbrrtee-, auapticmlvsicseeo.hrmdimTeesphveaeneornltfoe,iafpeoodbmrnebeeo,yrnreatmtdshoaiebftlyvPpiosorurolkstyp,neaexockrawoptnivnhe',esbs,nveeootxhcmrpoteeenexenrsxiiampdpiheeenrerneinptmdosla.measnBsmetnyqaaauvcmascirlhoeitotmduawie--owafcettiuhosneedlparstouecrcehossnco.pnecceupltiaarsittiehse,rmpraolcmeeadginngetiicncohuemr diceavlircee-, menItt wshiothuldthbeevnoortteexd pthhaetnothmeeenxapeexriemcuetnitona,ccionmclupdliisnhgeoienlnuegercrtdpgreyropomdbaearlemtgmmnoesentnsiitctnricaonltunitdeohsine,n,gIcfnoostrrthrieeetxsupaitnmoevnpoedsfleetmdi,gseautctochihoatnnhaiescoaafslubaebabnjlngelocilntirgsemheorat--fl ncestaxiinrplrlgey.rrieineqWgnucoieeruicntwrgseauasactlghel-adraiontwuehnodedr,krts,ehtlteuehvdevayacnloatunnaesdbxidlpdeeeerersaxicmbprlieeeprntietimxoapnelenbwrtiaameslrieefsanocftobtasr-l tained.
The idea of experiment consisted in prompt magnet
heating in the close antimagnetic cylinder placed in an- That's why we placed the special emphasis to the
1E-mail: [email protected] 2 E-mail:
enxopmeerinma.ents with possible occurrence of the vortex phe-
V.V. Balyberdin, A.V. Nechayev
Figure 1: The cross section of the container with a magnet Figure 2: The key diagram of the whole experimental stand
3. The description of the experimental device The cross section of the container with a magnet is given in Fig. 1. The container represented the cylinder from steel 1X18H10T with the wall thickness of 5 10 3 m and total capacity 0.5 dm3, which was closed by the lid 2 of the same steel mark. The holes are made in the lid including the ceramic tubes 8 and 9 for input of a nickelchrome burn spiral 6 and 7, disposed in an intermediate burning charge. Magnet 4 is in the dense lling of the termite charge 3. Non-gaseous ferrite-magnetic termite wstaasckuesdedonasththeecotenrtmaiinteerchbaortgtoe.mT. he ceramic tile 5 was drieTdhpeowcodnetraionfetrhceatpearcmitiyteims ixllteudrewiniththgrreien-qduedartweerlsl.- At layer-by-layer termite lling the magnet was put approximately half of the lling capacity. After lling and leading-out wires of a burning spiral outside through the third hole in a lid (not specied in the drawing) the chrome-aluminum thermoelectric couple in glass-ber isolation was introduced inside the capacity. The lid was xed by bolts on a container ange, then the container was interposed into other cylinder of greater capacity made of aluminum alloy. The key diagram of the whole experimental stand is given in Fig. 2. The cylinder 8 with the container 10 was hanged on aitttnheenrgbesa3otlraor1b-cm0toohrneea3natseosauccrntrhyeidendmwgleatenrol.ilgn.atgThTthw2ehenietmsbhoc.aryar-lmisinstedeaecesllruocrs8aienbdwgleahrsaoinrfhdgatlhny2egueaddpcicatoimonrdteao-- The interior capacity of the container 8 was lled with asbestos bril, and its outer surface was wound with asbestos cloth as a heat insulation and protection of measuring sensors around the container.
The inductance coil 6, the Hall's sensor 5, the tensor scales 2 with the tensor amplier 3 have been used as measuring sensors. The current recording in a burning spiral 12 was carried out according to power drop out on the shunt R, included consistently into a burn chain. The rectier BK-102 has been used as a direct current source. The recording of signal value changes from sensors was carried out on the tail oscillograph H-117 (point 4 in the Fig .2). Tensor scales represented a steel ring with the tensor sensors glued on an interior ring surface. Tensor scales were made by the experts of RPA called after Lavochkin, they were calibrated by him as well allowed to execute the force measuring of the value up to 100n with an error not worse 0.1n. The scales provided the precision and dynamics stable, warranted by the developer, as the further investigations have shown. The order of the experiment accomplishment was the following. Before each experiment and after it, 10 experiments were carried out, the calibration of scales and preliminary checkout of the serviceability of used measuring means was executed. After that the oscillograph 4 was included into zero lines broach, and only having executed this operation, they included the burning current of termite mixture. The magnetic rings of the alloy UNDK2A (2 pieces) with external diameter 6.5 10 2 m, internal diameter 3 10 2 m and thickness 2.5 10 2 m, and also ferrite magnets from loudspeakers with the diameter on the outer surface 90 10 2 m, the interior surface 4.0 10 2 m were used during the experiments. Maximal value of a magnetic induction: on the magnet surface UNDK is 250 mTl that corresponds to a magnetic enemisrgTTylK,Ea=Mn1d4E940.M56CJ1,;.f4oo6nr9fteJhr.eriTtseuhreifsaCTcueKroie=f fp4e4orr5initteCfr.oirnTgUhseNrBeDiKs12n1A7o
Figure 3: The oscillograms were obtained during main experiments
magnetic induction after burning. dthiouIcnguhlttyhoueorffortshrtme eemrxpaegexrnpiemetriiezenentdcsetwewremithcitoesnimfmroiilnxattreudmreiwxbtiuutrhrneitnehxge-, ctcbahluuumerrdrnabeeingdunntrgtnehatdienc)i.cdgporrinendosiiuttnipgacplatyiouossfnieon.rgdWbiouefrcchnuoailmndtigept.sloiciTinanhtcteirhoenteaessrteomescvtictosuelr(trmwaegniitexchteaounuardett athsbeeIntsetscohessosuablrdryilbseatabngooevt,eeadts,httehhecaotpnotthwaeienrcefournlwtvaietirnhteiacramllelaingnguexwti,oitnwhao8sf shtjeohotmelewteseaiirsnnmcrteaihtsneetdrcmieocsnitcxetetdanuitnbreeyprrbtoluhiddreunwlciantibstgho.trhaTartmhooueragyglhencneeogtintlwihenagoosffhotaebhnisgeeehrrtveuse(esd2irnvamget apcqabubrmooardivnleuetwicottatuyhss.te.aolpAafpbstlohiaeredartoetosuorutyelextrtcatlchbuoeldneet)aa.tpihnTpeeehrareerdainiclgtliuinvbsegeulfroyonfriactnnhegdeopfairnrsoebddsem-ushtcaootlsstl outTthhee inmvaetsetrigiaaltimoneaonf sthleacskimhialasrneotuaxliloonwoefdthcaerbryuirnng-
iinngg pprraocdtuiccatsl rinesuopltesncoautmldobspehoebrtea,itnheoduignhtthhies cinatseer.est- 4. Results of experiments Tmheentso,stcwillooogfrawmhsichwaerree goibvetanininedthdeuFriign.g3amaanidn Feixgp.e3rbi-. withThneumsiegrnaalslsinofotshceillfooglrloawmisn:g data units are marked 1 | tensor scales; 2 | Hall's sensor; 3 | inductance; 4 | signal from the resistor R; 5 | signal from the photodiode; 6 | signal from the thermoelectric couple. nanetdiDcmeisanpgdintueecttoiicfontihnedthumectarigoendneutrcietcgioirsintnegorsefdutshbeeywctiohthnetvHaaianrlielor'suwssemenigsaohgrtacinlldoginradmucst.ance coil is registered distinctly in both osmenTthoef ltinhee Ithienrmthael Fmiga.gn3eatimzaatrikosn tdheestbruegcitnionnin, gwmheon-
90 tphoeinMtteovmraeplueseeranotsfuittriheveewagalalrolmvya.inngomueptehraws aesxcineecdlueddedthientCoutrhiee channel registering the tensor bridge misbalance and ittthhaeistfrwaeqlellulseysnescetynem5bsHotzbh,etgirniannastnfoerocrshicnaiglnlogingermaapsohroeashcniidlglhai-tnfiroeFnqisug.ewn3ictbhy, ones with the considerable component constant. The signal from the photodiode seems interesting, it sVhiosuualdllyreancotetxohhaoutstgsaswesereexhobausesrtvsefdro, mhotwheevceornptahionteord8i-. othdee pbeerfoiorde mix1t0urseecb,uarnndingchgaanvgeesdiginnalapsuelqsuaetinocnes: w3i.t8h; 4ti.o0n;s4;.8a;n.d..uspectoaftthere tinhietibaulrvnailnuge.pIenrioodthoefr twhoersdeso,stchilelraewere some energy processes in the ambient around the ccoanmteaitnoera,ntheqisuislpibarcieumaresatawteasduinrinagn 7e0x{c9it0edsecs.tate and 5. Conclussion Unfortunately, due to the lack of sucient magnets qvthauerairnomtuiostyemleocaftgvrnaiceritcoiocuusppmrloeapsg,enrwtehiteiiscc,hmlcaaoctukelrdioafblsheaigdnhids-ptaeocmsceopdredirimantgmutreoediitnnaiasfionttBrreeumrleysmcaamoetuinnosatensmastowai(fougasnnpst,ernttotoonhbt5geoodksbcuigotes)ansp,isinetildneiwmdesira.oiastnbendlaeonntsdaphtoacusorrseneibsooildffeerttreohagebioslbetuesscereoirfnvnuge-l ttinhhteeeWremrxeeaplgaceontcinteoetsndiicdocerforitnnthgtheaeaimntoeebirtctsharaiodnnteeaiscdttairorluenacsntuaidlortonmsua(nawsgdepnarementlieicamamxniinaoplamhrlyiyennsaeitcnsoa)dfl. qfticoeualmallo1liwic.tshainoTatbigrhvgseceeeo,rpvnbboecuudwltru,neasrniitnoeitngvnhsete:aretnrshatdecaltgceieorsysno,sftiiattnhlilestinrhpmeeoasemslximapbgleaenrgietmntoeemtsnitctraaucklchetseutymhrsee-dmeastg2rn.ueTcttihicoemnp.aotwereirailnstweriathctmionajeorescpteicsimcoerneeerxgpy.ressed in dpiroodl34oe..nTigsTehodheb.easeirnevcvetedsutpiingoantthipoe-nnzsotnrianenatshritoiisuonnddsiritnehcaetisocenomnsti-hacioonuneldrd.ucbteor Acknowledgements IcnollceoangculeussiMon.Fw. eSleoxbpordeesnsuoku,rI.gVr.aBtiteursdheovtao,oMur.Kf.orBmoyeralthaoneblRpfoorPriaoAntuhdseemerhxepespllepeoaryriiencmehspenrscetuapspl,alpeardoasrtwati,ofetnlealrnawdnLedadevcxioaspccrruhreyskssiisninogonbuooruotgtfhrotafhfotetirthutoehdbseeetained results.
V.V. Balyberdin, A.V. Nechayev
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 91{94 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
PENETRATING RADIATION OF CAVITATION CAVITIES V.V. BalyberdinN, V.T. Glyanko, N.A. Zhuck1 N, N.D. Kolpakov , A.V. Nechaev|N, S.I. ChernyshovN N Research and Technological Institute of Transcription, Translation and Replication, JSC, Box 589, 3 Kolomenskaya St., Kharkiv 61166, Ukraine Kharkiv National Technical University of Radioelectronics, 14 Lenin St., Kharkiv 61726, Ukraine |A.N. Podgorny Institute for Mechanical Engineering Problems of Sciences National Academy, Kharkiv, Ukraine Received June 10, 2004 The schemes and descriptions of experimental devices as well as the experiment results of radiation recording transiting through metal screens and having not even precisely obscure nature are given in the article. 1. Introduction Ttcuohnreesipdarveerasaiulbaplbeploepseittneieromtnraeodtfinaagds dapibtoiilloaitnryiazlwartaaisodnisattoaintoeendatbynypdethhianevaninuag-tgkaEhenalnooorretwtrhionan.ft,tiasTohinnmehdipaislianatvpdrwaergrraaeus[dce1poin]ar.oendssHtsissniobglwbeleodeotvofhoensrnliiymnltyhtiselotpaomagrcuteteheytshepasose,odwtprshepeomalolftraarttiauhsndneeoiridnaetytutaiohnronee-f amectahsuoadlofnidtsorfecaorldaibnogr.atory radiation source and the uofsasgStaeurcahspypssilttieuemdatsbio[y2n]Naa.lsAsot.hKheoazrseypcroerevrddfienotregrrmoandieni.aedtiotnhirsemcoertdhinogd
2. The Experimental Device Construction Tfhlaoyhbrdeorcrohhadeytcyodknrroyoaumdrtyaindcoaifsamyntshtitceesrmocmousnrawctleoa.pushrcyhwsoiicstaehlnaealcmeacvotissttyocfnasocuzaazvllieltyautasisoedna caviTtahteiokneynodziazlgeraismgoivfehnydinrotdhyenFaimg.ic1c.ontour with the According to the experimental device construction, ictsthuenepcrtopmrnliyfsauiltsgotacsotlhoupefpultpmehuepmout(prt3al)(ey,7t)sm(,1(fo)e6,ue)tde,hletpc(uit4pbr)eie,cliocneafenvhgiyotidfantreriaeo(uvn2le)ircmswmeeistehlhdiqi(tuu5him)de, (sd8ye)s ,teecbmtiob(rb1o0(f)9,t)sh,cerheeownsgecilnaoemf vpaein(r1t1irle)a,lteriaoespnela(f1cr3eoa)m.blemlleadgnpeitp(e1li2n)e, 1E-mail: [email protected]
Figure 1: A key diagram of a hydrodynamic contour with a cavitation mesh The ow diagram of the experimental device includigmneginc:errotavhtoeolrtimrorfeatwdeiaravtoeesfd(a3re)d,siissrtteeocetrl a(c1nu)dr,rdernieet lee(ccVttor)ir,c toshcfreweremanvasels(4c(,o25u))-,,
V.V. Balyberdin, V.T. Glyanko, N.A. Zhuck, N.D. Kolpakov, A.V. Nechaev, S.I. Chernyshov
Figure 2: The ow diagram of the experimental device
Figure 3: The time course of water temperature change in the contour
ple miliampervoltmeter (mV), counter of electric energy (EE) and Winston's bridge (WB) is given in the Fig. 2. The glass parabolic mirror with aluminum coat of the diameter 0.5m has been used as a re ector. The resistor of the mark MLT-0.125 with the resisttaonr.ceTRhe1 =re4si.s7tokrOwmaswpalsaacepdpliinetdoatshtehree reeccotordr ifnogcures.sis- Other resistors with an opportunity of their adjustment for Winston's bridge balancing were placed inside a foam box and outlets of otake wires to the resistor Rba1ttaersiewseollf a9sV)inwtaekree wcoinrensecttoedthteo pthowe emr assuspivpelym(etthael plates xed on a dielectric. This connection allowed hoping for the lack of heat in ows through wires to the resistors inside a box. The microvoltmeter of a direct current TR-1452 (produced by the rm TESLA) was used as a recording instrument. For excluding of any luminous uxes penetrating onto the recording resistor, the mirror (re ector), the recording resistor and screens were covered with a black thick cloth. The recording re ector and resistor were removed from a hydrodynamic contour in the distance of 3 m. 3. Results of Experimental Investigations Tlohwes.experimental investigations were conducted as foldwyansTadmheetieccromcnoidnntietodiuorbnyswowefreecllafivutieltraaltltieeoddnawotcacttuherrerheneracstetinisngtaiagneha,ytcdharavot--
itation mesh registered by "chromel - kopelev" thermoelectric couples of the diameter 0,310 3 m. distilled water was used as hydraulic medium (the contour volume was 0.65 litters). The results of temperature rise during contour running are given in the Fig. 3. The time course of the contour temperature change is well iterated in the same uid and diers essentially while various water solutions of salts using, at the heavy water additive and aqueous stream magnetization going to a cavitation nozzle. The water pressure in a contour at the work beginning is 0.15 105 Pa, through 600 sec is (0.45{0.5) 105 Pa. To understand, what occurs in a hydrodynamic contour and what the cavitation section means, a direct copper tube was included into the system instead of cavitation section, equal to removed section as for length, with the diameter and interior section equal to the diameter and the socket interior section aotf stuhcehcarevpitlaatcieomnesnetctiisonsminalleletr. cAonnnaepcptianrgenmt edtealcmienascsy, that should result to more prompt heating of a pipeline system, if the heat release reason was in other radiant, rather than physicochemical processes in the cavitation uid. servTedheinwtahteerextepmerpimereantutsrewritisheaindaireccotnttuoubre w(eavsennowtiothb-oauctomntaogunrehtiacsceoldnsaideercat)b,lyanldowthere vteamlupe,eriantucoremvpaaluriesoinn with a cavitation mesh available. We succeeded to increase the water temperature in a contour up to values 70C and more during a lot of experiments, but we restricted to this temperature limit taking into account the pump electric engine heating without wishing its preliminary failure. The execut-
Figure 4: The time course of water temperature dependence and signal value from Winston's bridge
est(uhid.pee.eptslmrtiaiemodnrsaeeftolteirohcmnatrsnaicto1iaof1ln0tehn%ceeo)ret,grytahcniainsetfntoobtremtvchaaaelmtruimoeenatolhfeeomnPceoio,ertnheacaptyvohevao'gnfsivot1heb.n1escearvviatatitoionnctornanrsmfoarmtioantioanbo[3u,t4h].igh eciency of energy eratTinhge tliinmeearistermecpoerrdaetdurperaincctirceaalsleyfirnomalltheexpsyersitmemenotps.- The multiple radiation measurements from a hydarnanratodmhdeeiycrxncctalhomunadtniecofudrcrooo.munbtotthsuerinphrtaohvceeeirssecenasosuougcachltuyrcrlaiennagdr ionrtehapeehraytndaarbtoiuldirtyey-, andTshigentaiml veacluoeurfsreomof twhaeteWr itnesmtopne'rsatburriedgien raesciosntotrouirs given in the Fig. 4. sistiegsqnudIateelncicrsthesnaaiesgnecng,eaesalsfnadrdroeymvtihtaotathtinoetonrhteeetso,ivsttathholauertez(tUeUhr)=oe i1mgs6isvatVerinkpuwwcloiaatutshreasdtechcneoeofpstuttbehbdyeathsethmeirceraovdoinltgmbeatlearnscceadlei.ndication before measuring on risseetlreavArteeidsod.niftroocfamrnatdbhieeatshieyoednnrosfirdgoynmnaaltmhoeciccduciroarngetrnoacumer,aotnphdeercalhetgaioinbngleeiscroeobgr--- However the signal value course after the pump sTgtehonpeerpreaintisignaginnsittmrhuepcrtheuysrsdeiroofnodrtyhsnaoatmmteihcteicmcoonent.toouurr irseminaexinpsliacsabthlee. of rTadhieateixoencustigednailmcphraonvgeems ebnyt othf ethseigrneacol rrdeicnogrdsicnhgemone aexrpelcoorredderrahdaiastaiollnowcheadratoctern.d out new features in the evidIennptacrhtiacnuglaers, ethveensigantarlavtahleure samndalclh(alreassctethraunnd5er%go)
additives to water, circulating in a the hydrodynamic
contour, alkalis or salts.
The time course of the signal value change from
the Winston's bridge resistor for water solutions of
y(wNtatHteer4rbOi(uHHm2),Obp)rooitsmasgisidivueemn(YicnhbltBohrrei3dF)e,i(gK.a5mC.lm) aonndiupmurheyddirsotixlildede
And if the sucient equal course of signal change
dependencies for solutions KCl and contain the information, enough for
NuHse4 iOnHthdeoseus bnsoet-
quent radiation generators, so the signal from water
solution of ytterbium bromide enables to think a lot
about the radiation generation features.
The numerous peaks on a signal curve allow speak-
ing about interesting radiation generation features in a
cavitation cavity as the solution temperature rise. Since
Of course, it is dicult to notice the amplitude
swings (by virtue of inertial properties of the point-
er device) at visual recording of signal value changes
ofaniltuhreesminicrtohveoslitgmneatlerg,entheerarteioconrdineraennaubplpeedr ocbusrevrevifnogr
pure water signal even in water.
esaicoxcmtecicTooeunnhtiteenwosduaietirtnhtteleotrrmhamcadepititnriasoeat ntciooeybncutienocnhorditnnemhcdreesatnttpahternrreoaidabtrlielwsoe ,mnheaacsottonotfrhrotrelhagehdeayvtirahdeetersitooihrsdnetey oivnrenacatltlmeeuorfert--
diminution of the registered signal that missed expec-
tations of its essential diminution.
The recording attempt of -background possible change
was made at the device running during investigations.
The used dosimeter "Jupiter- SIM-0.5" did not register
V.V. Balyberdin, V.T. Glyanko, N.A. Zhuck, N.D. Kolpakov, A.V. Nechaev, S.I. Chernyshov
Figure 5: The time course of the signal value change from the Winston's bridge for various operating bodies in a hydro- dynamic contour tdrheoceeosrrdanidonitgoeaxicnctslituvrdeuembtaehcnektgafartocioutnnthdwaiitlnltcghrieevaeusseoe,thobefurmtroeitsr,uelhsteosn.wseitvievre, 4. Conclusion Toipnuuhgsteraemenxasoeswcroeunertsqehdauabeivsonteuviotnensottsthigaetalhltroaieowngniessrdt,eecutroeneidfvroeercdrteauidvanienaastttweiholeeynr,ssidn.nuagetlTuetrhomeeveaaaanrunid--thcmhaoalowkrpesirvnoehgbral,tveotmeheessxyopinmewrteiihlmlevreaaenrfritrtaaainclitnldesafirotnoafmo.trhdpeeoorlreoemtfitcichaelasgerxfeoparltatenhsatetotirroeuntsist-, aprcaotridueosiOnnauttnptitepoyhnoptesheiensuin ntoghufpaeeievnsncocdarenaroeeubufwplbueotltlniebenscia sholumin-veoenetldhcooeiegrcgiaodcalafenltirineesocvmgpteiipsssottotneiragrtkaeoudtifnnionigrtneaiiwednositf,arotaatiahdnociidns-upon some investigators. References [1] N.D. Kolpakov, \Polarization waves." Radiotekhnika, 101, pp. 53{62, (1997). [2] N.A. Kozyrev, \Astronomical observations by time Physical Properties." In: \Flashing stars," Yerevan, SA of Armenia SSR, 1977, pp. 209{226. [3] L.P. Fomynsky, \How the Potapov's vortex thermal generator runs," Cherkasy, OKO-PLUS, 2001, 104 pp. [4] L.P. Fomynsky, \Supersimple thermal generators against Roman club," Cherkasy, OKO-PLUS, 2003, 424 pp.
Spacetime & Substance, Vol. 5 (2004), No. 2 (22), pp. 95{96 c 2004 Research and Technological Institute of Transcription, Translation and Replication, JSC
Jorge Guala-Valverde1y & M.F. Najarz
y Subsecretaria de Energia del Neuquen-NQN. Government, Argentina z Ejercito Argentino, Argentina Received August 28, 2003
We analyze, for the rst time, energy conservation as applied to homopolar electromagnetic devices. Our ndings, advanced in this journal (, 3, 3 (13), 2002), disprove wrong statementsrecently appeared in the literature (A.L. Kholmetskii, Am. J. Phys., 71, 6, 2003).
1. General Force and Torque Considerations
free energy believers sustain the possibility of energy extraction from the space with the aid of homopolar generators. The above unphysical expectation was suggested by N. Tesla himself (1) and advocated by B. De Palma, P. Tewari and others (2{6). The correct physics of homopolar induction (7 and references therein) allow us disprove such naive expectations. Figure 1 sketches the essential components of the ancient Faraday (Maxwell) homopolar generator (motor): 12)) AAcmonadguncettincrgearatidnigalabnaruanbifloertmo rBot-ateelda.bout magnet's symmetry axle. The ends of the bar are terminated as contacts able to slide, respectively, on the axle and3o)nAacl(orsaidnigu-sciRrc)umitewtairleli,ctrhiengcl.osing wire from herein, also terminated as sliding contacts touching both the axle and the outer ring. When the bar is spun on the magnet, the bar itself becomes an emf source able to drive a DC across te entire closed circuit (bar plus closing wire). Torque (due trematoonneiatlsttdilehhrw.tqeeeoouHbmmtraeahtaarlhreeggbgbnndBuiaeervtrtte))=asomaanpcc(deMttIpasiBni=todthtnmerheI)teetrchobegn,raeMwaiRnrng;itCstr2eeeeoWvgg.f2amrBTa=lfuethoweenred.thatMliwaMocclhcooo;oaBrnni(tesegseo(qtndvdatuoeuhnaarreett-,l but opposite) reaction torques acting on the magnet, thBe;Mabaonvde toCrWqu;Me rpelraetciloundsesweitsseolewcnt trhoteaftoiollno.wFinrgomonael,l
= M;B CW;M
1E-mail: [email protected], [email protected]
Figure 1: Faraday-Maxwell's Setup Magnet Bar and Clos- ing Wire in order to clarify further energetics considerations. When the bar is attached to the magnet and both co-rotate, the bar no more works as an emf source. The closing wire (at relative motion with the magnet) becomes now the emf source. Being the bar attached to the magnet, and due to the action-reaction cancellation, ttthaoteitothnoer.qTuclehosesitnMogr;qBuweainrdeC,WiBs;M;Mthaeacrtreienspugononansbilbtehleteofmoprarogmdnauetgcenderuto'esrotation (8).
Jorge Guala-Valverde & M.F. Najar
3. Conclussion Asogseuursroetvuwpadnuetidltislosssna.acsplwAaienoialmrlrokecrswdduaihsnbtteoaynamrlysloaoi nrmnyueehxmio-savmiuasartcobyhoplioneonrclgsaetopre(nt9dirg)oeeivncnlioasecgcseakn,sb.iezoonOefuetvrptgehhtryayhutsecniociaitnasyn--l uelneicftorrimc reoltdatininigtsmvaicginneittyin(1d0u) a Lorentz-like radial Acknowledgements TtaoncCe..N. Gagliardo and O. Cabrera for helpful assis-
Figure 2: The bar rotates in the CCW sense (red arrow). Braking force on the bar (blue arrow) diminishes its kinetic energy
2. Energetics
1pa)ocleBenaotrfritffhureegeamltaoDgCrnoe.ttaAatltesorientshtteihnecltoChseCinlWagbw(sierngesurereemo2na)itnghesenaentroarrteteshst in the lab. The bar is acted on by the CW sense braking
force F = RRIB dr, which diminishes its kinetic energy 0
aboTveh.isInfoorrcdeerptroodkeuecpesthteherottaotriqouneal aMng;Buladrevseclroibcietdy
!me(crhaadniaicnaslpeenresregcyonmdu)sctodnestliavnetr, pthoeweexrt(ewrnaatltss)ouartcethoef
= MB! . Energy
the spinning bar and themagnet (both at relative
2) Bar attached to the magnet, both spinning in the
CCW sense; the closing wire at rest in the lab. Now
energy transference takes place between the spin-
ning magnet and the closing wire. Being the bar at
relative rest with the magnet, it only plays a passive
role (to provide a current-path). Customary physics
don't prescribe how the forces produced by the closing
wire on the magnet are distributed on its bulk, which
make impossible the direct calculation of the relevant
ttohrequmeagCneWt;.MNgeevneerrtahteeldessb,yotuhre fcolromsinerg awniraely, saicst,ineqguoan-
tion 1, ensures the mechanical
consequently, order to keep
rotational kinetic energy constant must be the same as
in the case described in paragraph 1.
References [1] [2] [3] [4] [5] [6] P. Tewari, New energy technologies Journal, 9, nov.- dec. 2002. [7] G.R. Dixon & E. Polito, [8] J. Guala-Valverde, P. Mazzoni & R. Achilles, Am. J. Physics, 70, 2002. [9] [10] J. Guala-Valverde, Physica Scripta (The Royal Swedish Academy of Sciences), 66, 2002.
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Spacetime & Substance
Volume 5, No. 2 (22), 2004
W.B. Belayev and D.Yu. Tsipenyuk. GRAVY-ELECTROMAGNETISM IN FIVE DIMENSIONS AND MOVING BODIES IN GALAXY AREA . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Angelo Loinger. ON THE ORIGIN OF THE NOTION OF GW ET CETERA . . . . . . . . . 53
N.K. Lohani MIXING . . . . .
and ....
Lalan ......
Prasad. ........
.H. .E.A.T. .IN. .G. .O. .F.
S. O. .L.A. .R.
.C.O. .R.O. .N.A. .L.L. .O.O. .P.S.
.B.Y. .P.H. .A.S. E. -
Dumitru Pricopi. A COLLAPSING POLYTPOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
V.R. Terrovere. DIONIC THEORY OF MESON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
I.M. Galitsky. NOSES WHICH
.P.R. .O.G. -75
V.R. Terrovere. STRUCTURE OF PHOTON & LEPTON . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Rasulkhozha S. Sharaddinov. MASS OF THE NEUTRINO AND ITS CHARGE . . . . 83
V.F. Barybin. THE CONTINUUM IS STRUCTURED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
V.V. Balyberdin, V.T. Glyanko, N.A. Zhuck, N.D. Kolpakov, A.V. Nechaev, S.I. Chernyshov. PENETRATING RADIATION OF CAVITATION CAVITIES . . . . . . . . 91
Jorge Guala-Valverde & M.F. Najar. BRAKING FORCE AND ENERGETICS IN HOMOPOLAR GENERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

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