Towards an Absolute Cosmic Distance Gauge by using Redshift Spectra from Light Fatigue.

Transcription

1 Towards an Absolute Cosmi Distane Gauge by using Redshift Spetra from Light Fatigue. Desribed by using the Maxwell Analogy for Gravitation. T. De Mees - pandora.be Abstrat Light is an eletromagneti wave with a dynami mass, and with a zero rest mass. A fourth parameter is gyrotation, the seond field of the Newtonian gravitation, disovered by using the Maxwell Analogy for Gravitation. Here, we apply gyrotation for light. The dynamis analysis of the gyro-gravitation parameters for light turns out in the possible existene of a very tiny light fatigue and a very tiny redshift as a diret onsequene. This redshift however is frequeny-dependent, unlike the other auses for redshift, as the Doppler effet, the Ashmore effet, the gravitational redshift and the temperature redshift. The disovery of this quadratially frequeny-dependent redshift allows us to set up the basis for an universal osmi distane measurement gauge. Key words : gyrotation, gravitation, light fatigue. Method : analyti. Index 1. Pro Memore : The Maxwell Analogy for gravitation: equations and symbols.. The mehanis and dynamis of light / The mehanis of light / The dynamis of light. 3. The dynamis of the dark energy in the presene of light / The gyro-gravitational desription of a light wave / Compression of a light wave / Depression of the light wave / Frequeny-dependent redshift. 4. Disussion and onlusion. 5. Referenes. De

2 1. Pro Memore : The Maxwell Analogy for gravitation: equations and symbols. For the basis of the theory, I refer to : A oherent double vetor field theory for Gravitation. The Maxwell Analogy laws for gravitation an be expressed in equations (1.1) up to (1.6) below. In the 'gyro-gravitation theory' (or 'dual field gravitation theory' or 'Maxwell analogue gravitation theory', et...), the eletri harge is substituted by mass, the magneti field by gyrotation, and the respetive onstants are also substituted. The gravitation aeleration is written as g, the so-alled seond field or gyrotation field as Ω (dimension [s -1 ]) and the universal gravitation onstant is found as G -1 = 4π ζ, where G is the universal gravitation onstant and ζ the gravitation onstant that is equivalent to the eletrostati onstant ε. We use the sign instead of = beause the right-hand side of the equations auses the left-hand side. This sign will be used when we want insist on the indution property in the equation. F is the resulting fore, v the relative veloity of the mass m with density ρ in the gravitational field. And j is the mass flow through a fititious surfae. F m ( g + v Ω ) (1.1). g ρ / ζ (1.) ² Ω j / ζ + g / t (1.3) div j - ρ / t (1.4) div Ω. Ω = 0 (1.5) g - Ω / t (1.6) It is possible to speak of gyrogravitation waves with a transmission veloity. = 1 / ( ζ τ ) (1.7) wherein τ = 4π G/. (1.8) τ is the equivalent onstant to the magneti onstant (permeability) µ.. The mehanis and dynamis of light..1 The mehanis of light. Light owns a dynami mass, but not a rest mass. In that ase, light must make use of a mass whih isn't its own, but has to earn it from some medium. It borrows mass. The name we give that medium isn't important here, so let us all it dark energy. Light an then be seen as a ompression of the medium itself, running at a veloity, whih is only dependent from the mass-density and the energy-density of the medium. The same equation for the wave veloity is then found, idential to the one of fluids: = E ρ ( E is the energy-density, similar to an elastiity fator, ρ is the mass-density) E = m whih is the same as saying that. The idea here is that the entity mass as well as the entity dark energy are of the same kind. This gives a physial meaning to the famous equation, for light.. The dynamis of light. Let us onsider a light wave, traveling at a veloity through the dark energy. A onsequene of the propagating mass wave in the weak gravitation field of the dark energy itself is that, when the wave propagates at a veloity, the ompressed dark energy will almost instantly jump from a very low mass-density status to a very high massdensity, and bak again to the low density. This jump will result in the reation of a gyrotation field Ω, that is De. 009

3 irular and perpendiular to the motion of the light, as explained in A Coherent Dual Vetor Field Theory for Gravitation. In fig.1 is shown what happens in the weak gravitational field g, if a mass-flow (whih here is direted towards the plane of the paper) travels in that field g.. m Ω g A moving mass in a gravitation field will generate a seond field (analogially to eletromagnetism) that is perpendiular to the gravitation field of the moving mass. Fig..1. Sine the sudden hange of mass (pulse) ours loally, the gyrotation field will be a loal pulse as well. At a ertain plae, on the light's path the pulse first grows to a maximum, and dereases bak to (almost) zero. y Ω Ω Ω Ω Ω x Fig.. A light wave, traveling in the positive x- axis' diretion will generate loally an inreasing gyrotation field during the first half period of the wave. During the seond half period, it will generate a dereasing gyrotation field. For a ertain loation, this results in a inrease of the gyrotation field during the first half period of the wave, and a derease of the gyrotation field during the seond half period of the wave. 3. The dynamis of the dark energy in the presene of light. 3.1 The gyro-gravitational desription of a light wave. Sine the hange of mass ours loally as a pulse, the gyrotation field will be a loal pulse as well. But if we follow the wave, the value of the gyrotation pulse remains a onstant, and in ourrene, it equals to the maximum value of the pulse. While the gyrotation pulse travels with a veloity, and the medium has a veloity zero (referene), the relative medium veloity is indeed. Applying equation (1.1) results in the generation of a ylindrial gyrotation fore whih ats on the medium, as shown in fig.3.1. De

4 v rel = - Ω y F Ω x λ Fig.3.1.a. Fig.3.1.b. A light wave travels with veloity and reates an elementary ylindrial gyrotation fore FΩ on the medium's mass, towards the wave mass. From equation (1.1) follows F = mv Ω with m = ρ V. Herein v is the veloity of the wave (in fat, the speed of light: ), m is its dynamial mass within the wave radius R, ρ is the density of the dark energy and V is the volume of the unompressed dark energy that is related to the eletromagneti wave. 3. Compression of a light wave. The infinitesimal work to ompress the light arrier, i.e. the dark energy is given by : dw = de = π F dr (3.1) For a given ylinder with length λ and radius R, on whih Ω ats, the total fore is given by : F = π λ ρ R Ω R (3.) Here, R is the radius of the unompressed dark energy volume that has to be taken in aount for the light wave. The wave matter that flows through the dark energy at veloity in a ylinder with radius R will be ontrated by the gyrotation that is reated by this flux. At the other hand, the infinitesimal radial displaement responds to dr = a t dt, wherein a g is the gravitational aeleration, wherefore we have the equation a = g Ω. (3.3.a.b.) This last equation follows from the physial origin of the speed of light in analogy with eletromagnetism, where we use the eletrial field E and the magneti field B, wherefore E B =. The value of the time t is only half the period of the wave or t = 1. Hene, from (3..a) follows that : g zr r = d Ω r = 0 4 (r R) (3.4) De

5 ² Ω j / ζ. The integrated Sine there is no gravitational soure we an redue equation (1.3) to equation, after appliation of the Stokes' theorem (see A Coherent Dual Vetor Field Theory for Gravitation, equation (.)), is : For a irular path about the light paket, this gives : Ω = G m r wherein &m is the derivative of the mass to the time. z Ωd l = 4πG & m (3.5) & h (r R) (3.6) Now, we an say that for light waves, we have E = m and E = h. At a ertain plae, the density of the dark energy hanges to the ompressed value of the light mass m = h. Now, we know that the mass paket of a length λ passes at a veloity of. The variation of the mass paket over time is then m t. And the time t orrespondents to the period of the light paket whih is the inverse of the frequeny : 1. m Hene, it follows that the mass variation equals to : t h = (3.7) Hene, we an rewrite (3.6) as : Ω = G h 4 (r R) (3.8) r And the elimination of from (3.4) and (3.8) gives : r G h = 3 (r R) (3.9) Sine this elimination results in a right hand that is a onstant for a given frequeny, we have to onlude that r = R. Remark that the value of the radius R is only dependent from the frequeny. Combining (3.8) and (3.9) gives also a frequeny-dependent equation : (3.10) Hene, (3.) an be rewritten as follows, when filling in (3.9) and (3.10) : 8 = G h 5 Ω 3 F = π λ ρ G h 11 (3.11) and the integration of (3.1) beomes, for a work W over the wavelength λ, sine we know that R is a onstant for a given frequeny : Wλ = π λ ρg h 3 6 (3.1) This is the work that is neessary for the ompression of the light over a distane λ. 3.3 Depression of the light wave. The depression of the wave, when the light paket of length λ passed by, should of ourse be the same value, but with a minus sign, exepted a very tiny part, due to the fat that in the real world, we an expet that the elastiity De

6 of the dark energy will show a very tiny energy loss. The value of this loss is unknown, and we represent it by the loss fator (1- ε ), wherein ε < 1. Hene, the energy gain by the depression is given by : Wλ = ε π λ ρg h 3 6 (3.13) Unfortunately, we don't know how muh will be lost. But anyway, the dark energy density isn't known either. In order to do not onfuse this with the tired light theories, whih are osmology theories, we all this effet light fatigue. Light fatigue is a very small redshift effet that is only a fration from the other auses of redshift. 3.4 Frequeny-dependent redshift. The equations (3.1) and (3.13) were found for a ylinder length of λ, but for a distane dx between the emission of the wave and its observation, we would get the following energy losses (we have put κ in replaement of the 6 onstants 1 ε π ρ b g G h ) : z z κ 3 dw = hd = κ 3 dx (3.14) o d Hene, = dx (3.15) e L 0 whih, after integration gives the distane L between the emitter and the observer: F HG L = κ o e I KJ (3.16) wherein the suffix o stands for observer and e for emitter. Equation (3.16) shows that the redshift of the observed light will be non-linear, unlike the redshift that is aused by the reoil of hydrogen by the Mössbauer effet, unlike the gravitational redshift, unlike the redshift due to the Doppler effet and unlike the one due to temperature redshift. An interesting onsequene is that for a frequeny spetrum of given isotopes, wherefore the values e are well known, the distane L an be found by the spread of the observed frequeny spetrum for these isotopes. When the linear redshifts have been subtrated, the remaining frequeny-dependent spetrum will orrespond to equation (3.15). It is true that the values of the dark energy's mass-density or its energy-density, as well as its inelasti part are not known yet. An estimate an however been found by using the equation (3.15) for already known distanes. 4. Disussion and onlusion. If light fatigue, due to the slightly inelasti dark energy, an be observed, it has to be quadratially frequenydependent. The possible presene of a quadrati olour shift for a very distant objet ould result in the finding of the real distane of that objet to us. Other redshifts are frequeny-invariant, suh as the gravitational analogy for the Compton effet (Zwiky) or Mössbauer redshift (L.Ashmore), the gravitational redshift (Einstein), Doppler redshift (Doppler) and the temperature redshift (J.Garía). After subtration of the frequeny-invariant redshifts, as a whole, the remaining small redshift an appear to be quadrati. If so, no other know effet than the light fatigue De

7 will explain it. After a number of suh observations, a relative distane sale an then be reated in order to find the loss fator (1- ε ). 5. Referenes. 1. Nobili S., et al. (The Supernova Cosmology Projet) : Constraining Dust and Color Variations of High-z SNe Using NICMOS on the Hubble Spae Telesope, 009, ApJ, 700, 1415, arxiv: Barbary K., et al., (Supernova Cosmology Projet) : Disovery of an Unusual Optial Transient with the Hubble Spae Telesope 009, ApJ, 690, 1358, arxiv: Garía J., Another Explanation of the Cosmologial Redshift, 009, General Siene Journal. 4. Ashmore L., Reoil Interation Between Photons and The Eletrons In The Plasma Of Intergalati Spae Leading To The Hubble Constant And CMB, Marh 003, updated August Zwiky, On the red shift of spetral lines through interstellar spae, 199, Pro. Nat. Aad. Si., 15, De Mees, T., A oherent double vetor field theory for Gravitation, 003, General Siene Journal. 7. Feynman, Leighton, Sands, 1963, Feynman Letures on Physis Vol. 8. Heaviside, O., A gravitational and eletromagneti Analogy, Part I, The Eletriian, 31, 81-8 (1893). 9. Jefimenko, O., 1991, Causality, Eletromagneti Indution, and Gravitation, (Eletret Sientifi, 000). De