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A New Formula of Redshift Vs. Space Expansion and Dark Energy

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A New Formula of Redshift Vs. Space Expansion and Dark Energy Journal of Modern Physics, 2021, 12, 229-253 https://www.scirp.org/journal/jmp ISSN Online: 2153-120X ISSN Print: 2153-1196 A New Formula of Redshift vs. Space Expansion and Dark Energy Olivier Serret ESIM Engineer, Cugnaux, France How to cite this paper: Serret, O. (2021) A Abstract New Formula of Redshift vs. Space Expan- sion and Dark Energy. Journal of Modern The speed away of stars and galaxies is traditionally calculated from the rela- Physics, 12, 229-253. tivistic formula according to the measurement of the redshift. It is demon- https://doi.org/10.4236/jmp.2021.123018 strated here another formula for this speed away of stars and galaxies, from Received: December 23, 2020 this same redshift z. After having exposed critiques on the demonstration and Accepted: February 17, 2021 the relativistic use which require the assumption of an expanding universe by Published: February 20, 2021 itself, it is proposed within the framework of neo-Newtonian mechanics the z Copyright © 2021 by author(s) and formula Vc= where V is the speed from the source. This formula has 1+ z Scientific Research Publishing Inc. This work is licensed under the Creative the double characteristic of being equivalent to relativistic predictions for low Commons Attribution International redshifts, but of deviating from them by up to 17% for high redshifts. It is License (CC BY 4.0). consistent with the observation of the anisotropy of the Universe and the http://creativecommons.org/licenses/by/4.0/ Cosmic Microwave Background. It helps to explain Pioneer anomalies. It is Open Access compatible with the constancy in the majority of cases of interference phe- nomena. Finally, it provides a new analysis grid for the observation of super- novae, galaxies and distant pulsars, thus opening up new fields of research on the increase in distances attributed to dark energy and also in other areas of the cosmology. Keywords Redshift, Blueshift, Dark Energy, Radial Velocity, Expansion of the Universe, Anisotropy, Hubble Law, Pioneer Spacecraft, Photon, Wavelength, Frequency, Variable Speed, Celerity of Light 1. Introduction In the past, the stars did not exactly follow the supposedly perfectly circular tra- jectory, it was necessary to imagine the existence of epicycles … until new ellip- tical trajectories were accepted. Today, the distant galaxies not having to exceed DOI: 10.4236/jmp.2021.123018 Feb. 20, 2021 229 Journal of Modern Physics O. Serret the speed of light in spite of the law of Hubble, it is imagined a space which would create itself its own space, and the distant supernovae not following ex- actly the speed away calculated there, it is imagined the existence of a repulsive dark energy … unless we come to accept a new formula for the speeds away as a function of the redshift. This is what we will try to demonstrate in this article. After having recalled the definitions and uses of redshift and wavelength, we will analyze the research status on the relativistic redshift formula. Then we will propose the neo-Newtonian derivation to get to the expression of a slightly modified formula. Finally, we will discuss the consequences or not of this change of formula. 2. Definition and Context The redshift, noted z, is the fringe shift measured on light and electromagnetic waves from moving objects. From this measurement, first the speed away for stars and galaxies is calculated and then their distance is deduced using Hubble’s “law”. Yet, at the horizons of the Universe, by correlating with the distances derived from their luminosity, supernovae appear to be at distances greater than those calculated by the redshift method (see Figure 1). To explain this additional dis- tance speed and therefore this additional distance, it is invoked the existence of a dark energy with a repulsive effect, dark energy which has so far not been able to be directly apprehended. And more simply, why not question the formulas used to calculate the very fast speeds and the far distances? Light and electromagnetic waves in general are characterized by their wave- length λ, their propagation speed c and their frequency f. We can characterize them only by two out of three parameters because they are related to each other by the relation: λ = cf (1) Figure 1. Schematic explanation of Dark Energy. DOI: 10.4236/jmp.2021.123018 230 Journal of Modern Physics O. Serret Since the speed of light in vacuum is assumed to be constant, it has become customary to characterize the electromagnetic waves by only one parameter, the wavelength λ (i.e. a distance). Yet this is the frequency (i.e. a time, or more ex- actly the inverse of time) that we perceive or directly measure. For example, an optical detector does not measure a length, but is excited at certain frequencies. This is why in this article we will favor the explanation by frequencies f (rather than by wavelengths λ). 3. Analysis of the Relativistic Redshift Formula The relativistic expression allowing to deduce the distance speed V from the redshift z is as follows: 2 (11+−z) = − Vc2 (2) (11++z) This formula comes up against two difficulties. 3.1. The Derivation Itself The usual demonstration goes through the following intermediate step [1] [2] [3] [4]: cV− λobs = (3) fobs The problem is that the theory of Relativity postulates that the speed linking the two quantities λobs and fobs is constant and therefore that the numerator must be equal to c in any frame of reference. This means that V should be zero, which is contradictory with a moving source. There are also few much more complex derivations, but the one we have seen [5] is also open to criticism (in this video, there is a mix between Galilean for- mulas and relativistic formulas and the Equation (3) is implicit). 3.2. The Expansion of Space Itself Even admitting the validity of the previous derivation, the relativistic formula only allows to relate the redshift to the speed by making an additional assump- tion, namely the expansion of space itself. This additional assumption does not appear necessary as long as the source does not move away at very high speeds because it is used a simplified formula. But when they are faced with very high speed or high z’s, they end up with an inconsistency that can only be overcome by posing the strange hypothesis of a space that expands by itself. Without this additional assumption, the relativistic Equation (2) of the redshift leads to an inconsistent situation on the propagation speeds [see Appendix 1]. 4. The Neo-Newtonian Derivation 4.1. The Neo-Newtonian Mechanic So what formula should be used between the distance velocities and the fringe DOI: 10.4236/jmp.2021.123018 231 Journal of Modern Physics O. Serret shifts received from high- stars and galaxies? The proposal falls within the framework of neo-Newtonian mechanics which is none other than Newtonian mechanics but without the principle of equivalence between inert mass and gra- vitational mass: thus, the increase of inertial mass as a function of the speed pre- vents the photon from exceeding the celerity c, this means that the speed of the photon would not be constant in any frame of reference. The purpose of this ar- ticle is not to detail Newtonian Mechanics, the reader may consult it in the RELATED LINKS [a]. And as in Newtonian mechanics, it is assumed that the photon is a body of matter that can move in a vacuum, and that there is a fixed or barycentric frame R0. 4.2. The Method of the Derivation The derivation is based on the redshift understood as an effect of the Dopp- ler-Fizeau effect. The Doppler-Fizeau effect can be described as the effect pro- duced by a moving source of electromagnetic waves in which there is an appar- ent upward shift in frequency for observers towards whom the source is ap- proaching and an apparent downward shift in frequency for observers from whom the source is receding. Here is a simplified derivation of the speed away as a function of redshift, the general derivation is given in Appendix 2. Let us take the usual and simplified case of a photon emitted from a source which moves away while the observer is motionless in the fixed frame of reference R0. The pho- tons (A) then (B) are emitted according to the time interval Tsource at the ce- lerity c in the reference frame of the source, but according to neo-Newtonian mechanics they move at the speed (c-V) in the fixed reference frame R0 (see Figure 2) vc= − v photon// R00 photon source source / R (4) v > 0 with source/ R0 . There are two ways to calculate the distance between photons (A) and (B): • The first way is to note that the distance λ between the photons (A) and (B) is the distance DA traveled by the photon (A) during the time Tsource added to the distance dsource traveled by the source until the emission photon (B) (see Figure 3) Figure 2. Velocities of the photon: in black/Ro and in green/source S. DOI: 10.4236/jmp.2021.123018 232 Journal of Modern Physics O. Serret Figure 3. Photons from the moving source to the observer. λ =DdA + source (5) λ = vT∗ + v∗ T A// R00 source source R source (6) • The second way is to consider that the distance between the photons is the propagation distance of the photon (B) until it reaches the position where the photon (A) had been observed at the time of the emission of (B): λ′ = vT∗ B/ R0 obs (7) λ′ = vf B/ R0 obs (8) In neo-Newtonian mechanics, there is no variation in distance or time de- pending on the speed of the frame of reference, the distance between two pho- tons is the same whether it is calculated from the observer or from the source.
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