A Note of Widening on the Redshift Mechanism. June 23, 2010.

Transcription

1 A Noe of Widening on he Redshif Mechanism June 3, 1. José Francisco García Juliá / Dr. Marco Merenciano, 65, Valencia (Spain) -mail: jose.garcia@dival.es Absrac A single ired ligh mechanism has been proposed for explaining he cosmological redshif wihou expansion of he universe and also he inrinsic redshif, ha is, he excess of redshif of he radio sources. In his noe of widening, we show ha he mechanism would be similar o he discharge of an elecric capacior, o he radiaion loss by fas elecrons and o he radioacive nuclei decay. Key words: cosmological redshif, inrinsic redshif, ired ligh. 1. Inroducion In a recen paper [1], a reasonable explanaion of boh redshifs: cosmological (wihou expansion of he universe) and inrinsic, is given using a single ired ligh mechanism. The mechanism supposed is he ineracion beween elecromagneic waves. For he case of cosmological redshif, he ligh waves inerac in he inergalacic space (IGS) wih he microwaves of he so-called cosmic microwave background radiaion (MBR). And, for he inrinsic redshif (namely, he excess of redshif of he radio sources), he ligh waves inerac inside of he radio sources (uasars, radio galaxies, ec.) wih radio waves. And all his is compaible wih a saic universe wih a space emperaure (of hermal euilibrium) of.7 ºK (which is he emperaure of he MBR). The mechanism would be similar o he discharge of an elecric capacior, o he radiaion loss by fas elecrons and o he radioacive nuclei decay.. The ired ligh mechanism The ineracion is a ransference of energy from he phoon o he microwave in he IGS or o he radio wave inside of a radio source, following a ired ligh mechanism of he form [1] ( ) e = (1) where is he energy of he phoon, he ime and a ime consan, whose value depends on he medium: = 1H, in he IGS, bu << 1H, inside of a radio source, 1

2 because he densiy of radio waves inside of he radio sources is much greaer han he densiy of microwaves in he IGS. I is similar o he discharge of an elecric capacior hrough he series resisance in an elecric circui [] (p. 47) ( ) e = () being he elecric charge, and he ime consan is = R, where R is he resisance and he capaciance. omparing (1) wih (), we see an analogy beween and. We can go beyond because ( ) e = (3) being he energy of he capacior (which is proporional o is capaciance) wih = R (see appendix). And he capaciance of a parallel plae capacior is = εa/ s where ε is he elecric permiiviy, A he plae area and s he plae separaion. Then, for he phoon, like an energy condenser, i would be s = λ, where λ is he wavelengh. And he rajecory of he phoon would be he circui. Then, and since 1 R = G is he conducance, = (open circui, R = ) would correspond o he mos resisive (leas conducive ) medium, he vacuum, and = (shor circui, R = ) for he leas resisive (mos conducive ) medium. Therefore, in he vacuum, he ligh would no lose any energy, whereas he cosmic objecs wih = would emi radio waves bu no ligh. However, we can consider our mechanism from a differen poin of view. Since he disance raveled by he phoon is c being he ligh speed in vacuum, and δ being a disance consan, hen, (1) is convered in d = c (4) δ = c (5) d δ ( d ) ( ) e = (6) wih δ =c H, in he IGS, bu δ <<c H, inside of a radio source. And, now, our mechanism, seen like (6), would be similar, from a uanum mechanical poin of view, o he radiaion loss by fas elecrons, where he mean energy of an elecron, wih iniial energy, afer having raversed a lengh x of he medium, is [3] (p. 74) [4] (p. 39) x X = e (7)

3 X being he so-called radiaion lengh, which is inversely proporional o he densiy of aoms of he medium. The euaion (7) is obained from he framework of reference of he elecron and considering ha his one scaers he elecromagneic fields (of he aoms of he medium) which ac like sreams of phoons. Therefore, comparing (6) wih (7) we deduce ha (in place of he elecron) our visible ligh phoon (acing like a paricle of effecive mass hν c, where h is he Planck s consan and ν he freuency) scaers (in place of sreams of phoons) microwaves in he IGS or radio waves inside of he radio sources, losing energy following (6) (in place of (7)). For las, as all he ineracions considered beween he phoon and he elecromagneic waves are analogous excep ha he energy of he phoon is coninuously decreasing, we may posulae, simply, ha in each ineracion he decrease of energy of he phoon is proporional o is energy, ha is d d = (8) dx d = (9) δ and separaing variables and inegraing we obain (1) and (6) (wih x = d ) respecively. Where (8) follows a law similar o he law of radioacive nuclei decay [3] (p. 176) N d dn = N (1) N ( ) e = (11) N being he number of radioacive nuclei and he ime consan is he mean life ime of a ypical nucleus of he nuclei sample. 3. onclusion We can conclude, hence, ha he single ired ligh mechanism proposed in [1] should be considered plausible because explains he observed redshifs: cosmological (wihou expansion of he universe) and inrinsic, and is compaible wih a space emperaure of.7 ºK. And, in addiion, i is in accordance wih various imporan physical phenomena like, for example, he discharge of an elecric capacior, he radiaion loss by fas elecrons or he radioacive nuclei decay. Appendix When an elecric capacior is disconneced from he baery, applying he Kirchhoff s volage law (and he Ohm s law) o he closed elecric circui, we would have + v = vr (1) 3

4 ( ) d R + = () d v R and he resisance, he capaciance, he charge and he ime. From () v being he volages in he resisance and in he capacior respecively, R and from (1), () and (3) R ( ) e = (3) v ( ) R = = e = v R ( ) e (4) i = d d ( ) R v ( ) R = e R = R e (5) i being he capacior curren. The discharge of energy of he elecric capacior would be ( ) = d = dp d = v i v = ( ) R ( e 1) d = v R ( ) e R d = (6) p are he energy and he power of he capacior, respecively. And from (6), we have where and ha is ( ) R v = e (7) ( ) v ( ) = (8) ( ) e = (9) and he energy of he capacior decreases exponenially wih he ime wih a ime consan R = (1) 4

5 Noice ha ( ) = ( ) e =. References [1] José Francisco García Juliá, A Brief and lemenary Noe on Redshif, May 6, 1. hp:// [] Joseph A. dminiser, ircuios lécricos, in Spanish, McGraw-Hill, México, 197. Original ediion, lecric ircuis, McGraw-Hill, New York, [3] milio Segrè, Núcleos y Parículas, in Spanish, Reveré, Barcelona, 197. Original ediion, Nuclei and Paricles, Benjamin, New York, [4] Donald H. Perkins, Inroducion o High nergy Physics, Addison-Wesley, Reading, Massachuses,