Journal of Theoretics

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1 Jounal of Theoetis Volume 6-1, Feb-Mah 4 An Altenative Exlanation of the Cosmologial Redshift by the Tahyon Plasma Field in Integalati Sae Takaaki Musha musha@jda-tdi.go.j, musha@jg.ejnet.ne.j MRI, , Namiki, Kanazwa-ku, Yokohama 6-5 Jaan Abstat: Fom the assumtion that integalati sae is filled with tahyon lasma, it an be shown that the osmologial edshift an be exlained by eletomagneti attenuation in the tahyon lasma field. Keywods : tahyon, lasma, osmologial edshift, zeo-oint flutuation. 1.Intodution The uent inteetation of obseved edshift of light fom distant galaxies is due to the exansion of the univese. Contay to this inteetation, altenative exlanations fo the osmologial edshift wee oosed by some eseahes[1-]. The autho has shown that the gavitational field due to the zeo-oint flutuation (ZPF) field an be anelled by the tahyon field eated out of the ZPF bakgound and almost of all enegy of the osmi bakgound adiation is due to the Cheenkov adiation fom tahyons eated fom the ZPF field[4,5]. In this ae, he also esents that the osmologial edshift an be exlained fom the assumtion that integalati sae is filled with vitual tahyon lasma eated fom the ZPF field.. Tahyon Field Geneated fom the ZPF Bakgound Fom the wave equation fo the moving elementay atile shown as i ψ h = m ψ +, (1) whih satisfies E ψ ( x, t) = A ex i t x h h, () whee ψ is wave funtion of the moving atile, is a light seed, h is a Plank s onstant divided by π, m is a oe mass of the atile, E is enegy of the atile and is its 1

2 momentum. By using the oe aeleation defined by = m αt, the solution of Eq(1) an be given by m ψ = C ex i + m log( m, mαh () whee C is an abitay onstant. Fom whih, the obability of the highly aeleated atile whih an exeed the light seed by quantum tunneling effet an be estimated as[6] π m T ex. ( 4) αh Aoding to the theoy of quantum mehanis, the emty sae is filled with vitual ati les, most of whih ae low enegy hotons m oving in an evanesent mode. Suosing that the vitual hoton eated fom the ZPF field is aeleated to the light seed inside the quantum egion with the size of Plank length l, we have α = / l fom the unetainty inile and m = h /, whee is an angula fequeny of the hoton. Then we have T π l ex, (5) whih shows a ossibility that the ai of a tahyon and an anti-tahyon eated fom the ZPF field in emty sae. By quantum eletodynamis, setal enegy density of the ZPF field in emty sae is given by [7] ρ( ) h = d. ( 6) π d The mass of vitual hoton eated inside the quantum egion with the size of Plank length yields the Plank mass m fom the unetainty inile shown as l h. Fom Eqs.(5) and (6), vitual tahyons eated fom the ZPF field an be oughly estimated as N h π l ex π m 5 d, (7) whee is the utoff fequeny of the ZPF field given by[7] 1/ 5 π =, (8) hg

3 whih has the ode of the Plank fequeny. By the numeial alulation, we have 1 N. 6 1 fom Eq.(7). Thus it is onsideed that emty sae is filled with ais of ositive and negative haged tahyons eated out fom the ZPF field if the tahyon has an eleti hage.. Eletomagneti Wave Taveling in the Tahyon Plasma Field Suosing that the integalati sae is filled with the tahyon lasma eated fom the ZPF field, eletomagneti waves below the lasma fequeny ae attenuated shown with the satteing of atiles in the lasma being desibed as[8] mv = qeτ, (9) whee is a mass of the atile, is the veloity of the atile, q is its hage, E m v is an eleti field and τ is the time inteval between ollisions. F om whih, the esonant fequeny of the tahyon lasma field an be estimated by[8] whee m is the mass of the tahyon defined by Nq =, (1) mε m = v m * / 1, (11) in whih, m * is an absolute value of the tahyon s oe mass. Fom the unetainty elation fo the tahyon given by[9] h t v the veloity of the tahyon moving in emty sae an be estimated as of the tahyon beomes, (1) v [5]. Then the mass h m, (1) l by using elations that m / and t l /. Suosing that an assumed hage of the tahyon equals that of the eleton[1], the esonant angula fequeny of tahyon lasma an be evaluated as (ad/s) at most by using N = Redshift of the ight fom the Distant Galaxies due to the Tahyon Plasma Field A oding to the eletomagneti theoy, eletomagneti waves in the lasma an be desibed by

4 E x u 1 E = u E, (14) whee u is the eletomagneti wave seed inside the lasma. By substituting E = A ex[ i( kx t)] into Eq.(14), we have k = ± i / u. (15) As the eleti field an be desibed as E = φ A / by using the sala otential φ and the veto otential A, the wave equation fo the eletomagneti field in tems of the veloity gauge as[11] 1 ρ φ φ =, (16.1) u ε φ A A = µ J +, (16.) u whee ρ is a hage density, J is a uent density ε is emittivity and µ is emeability of fee sae. Fo the ase when >>, the veto otential, the veloity of whih equals the light seed, is aidly attenuated and finally beomes zeo fom Eq.(15) and only longitudinal waves an oagate in the lasma field as shown by following equations, if the seed of the sala otential is muh highe than the light seed (see Fig.1). 1 ρ φ φ =, (17.1) ε 1 1 φ µ J =, (17.) whee is the veloity of longitudinal waves. 4

5 Figu e 1. Wave oagation in integalati sae. Suosing that thee is no tahyon lasma field in the sae nea the Eath, whee =, ρ = and J =, the sala wave is tansfomed into tansvese and longitudinal waves fom Eqs.(16.1) and (16.) shown as 1 φ φ =, (18.1) 1 A A =. ( 18.) Fom Eq.(15), we have k ± i / fo the hoton taveling in a longitudinal mode inside the l asma, whih fequeny is muh lowe that the lasma esonant fequeny. Then the enegy of the hoton taveling inside the lasma field is given by Ε ( x) = Ε ex( βx) = Ε ex x, (19) whee Ε is enegy of the hoton, β is an attenuation onstant and x is a taveling distane of the hoton. By the elation of enegy of the wave shown as hoton beomes Ε = πh / λ, the wavelength of the λ( x) = λ x ex, () whee λ is the wavelength of the hoton at the time of emission and λ is the wavelength of the hoton whih is obseved. When the value of / is negligibly small omaed with unity, the elation of the edshift of hoton and the distane x an be given by 5

6 λ λ = ex x 1 x λ. (1) Fom whih, the eeding veloity of distant galaxies an be obtained as v / x, () whee the seed of the longitudinal wave in integalati sae an be estimated fom the Hubble onstant H as H (m/s) () by making the substitution v H x [1]. Consideing highe tems of ex(x ), the veloity of exansion beomes / 1 1 v = x + x + 6 x +. (4) If we let = (m/s), veloity uves alulated by Eqs.() and (4) is shown in Fig., whee a hoizontal line is fo a distane fom us in billion light yeas and a vetial line is fo the eeding seed of the galaxy in km/s. Fom this figue, the alulation esult onsideing highe tems shows that the eeding seed of galaxies is aeleated with ineased distane fom us. Figue. Seed of the distant galaxy edited by the theoy. Reently astonome gous have evealed that osmi exansion is seeding u fom the obsevation of vey distant suenovae[1]. They onluded that thei obsevation esult is due to the eulsive osmologial onstant, but it might also be exlained by the attenuation of 6

7 eletomagneti waves taveling in the integalati tahyon lasma field as shown in this ae. 5. Conlusion In this ae, it is shown that the osmi edshift of light an be exlained by the attenuation of eletomagneti waves in the integalati tahyon lasma field. Fom whih, the eent obsevation esult that osmi exansion is seeding u an also be exlained by the exonential attenuation of eletomagneti waves in the integalati tahyon lasma field. Refeenes [1] P.A. aviolette, Subquantum Kinetis,Stalane Pubns,NY (1994). [] J.Petit, An Inteetation of Cosmologial Model with Vaiable ight Veloity, Moden Physis ettes A,16(1988), [] R.J.Hannon, An altenative exlanation of the osmologial edshift, Physis Essays 11,4(1998), [4] T.Musha, Possible Existene of Tahyon Field anellation of ZPF Indued gavitational Field in Emty Sae, Jounal of Theoetis,4(). [5] T.Musha, Cheenkov Radiation fom Faste-Than-ight Photons Ceated in a ZPF Bakgound, Jounal of Theoetis.,(1). [6] T.Musha, The ossibility of Neutinos deteted as Tahyons, Jounal of Theoetis 6,1(4). [7] H.E.Puthoff, Gavity as a zeo-oint-flutuation foe, Physial Review A 9,5,-4(1989). [8] R.P.Feynman, R.B.eighton, M.Sands, The Feynman etues on Physis, Vol.II, Addison-Wesley Publishing Co. MA(1977). [9] M.Pak, Y.Pak, On the Foundations of the Relativisti Dynamis with the Tahyon, Nuovo Cimento 111B,11(1996), [1] E.J.Betinis, Eletomagneti theoy Relativisti Shodinge Equation. Its Solution and the Satteing Coss Setion fo Sueluminal Patiles, Physis Essays 11, (1998), [11] D.M.Duy, The Unifiation of the oentz and Coulomb Gauges of Eletomagneti Theoy, IEE Tansations on Eduation 4,1(), [1] H..Andeson(ed), A Physiist s Desk efeene, The Seond Edition of Physis Vade Meum, Ameian Institute of Physis, New Yok(1989). [1] B.Shwazshild, Vey Distant Suenovae Suggest that the Cosmi Exansion Is Seeding U, Physis Today( June,1998), Jounal Home Page Jounal of Theoetis, In. 4 7